Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt
from itertools import permutations

def root_search(order, cost, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = [] #一段階前の確定した道順
    pre_hold.append((0, "0", set() | order, 0)) #cost, pass, left, id
    hold_size = 0
    for i in range(type_num):
        for pre_cost, pre_pass, to_search, pre_id in pre_hold:
            for key in to_search:
                heappush(hold, (pre_cost + wf[pre_id][key] / sqrt(cost[key][1]), " ".join([pre_pass, str(key)]), to_search - {key}, key))
                hold_size += 1
        pre_hold = []

        for _ in range(min(hold_size, 3)):
            pre_hold.append(heappop(hold))
        hold = []
        hold_size = 0
 
    ans_cost, ans_pass, ans_search, ans_id = pre_hold[0]
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)
 
    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_hold, wf):
    c = store_hold * 1000 / wf[current_id][0]
    for key in order:
        if cost[key][1]  * 10000 / wf[current_id][key] > c: return final_dist
    return 0
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i, j in permutations(range(V), 2):
            if wf[i][j] > wf[i][k] + wf[k][j]:
                wf[i][j] = wf[i][k] + wf[k][j]
                next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = dict()
    for t in range(T): command[t] = -1
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = [0] * V
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0
                    root_size = len(root_list)

            if heading in order:
                order.remove(heading)
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                for j in range(root_pointer, root_size - 1):
                    if cost[root_list[j + 1]][0] > 0:
                        final_dist = root_list[j + 1]
                        root_pointer = j + 1
                        if current_id > 0 and store_hold > 0:
                            final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf)
                        break
                else: final_dist = 0

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt
from itertools import permutations

def root_search(order, cost, current_id, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    initial = set() | order
    pre_hold.append((0, str(current_id), initial, current_id)) #cost, pass, left, id, time
    hold_size = 0
    width = (3 if V >= 350 else 4)
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id = pre_hold.popleft()
            for key in to_search:
                new_cost = pre_cost + wf[pre_id][key] / sqrt(cost[key][1])
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (new_cost, new_pass, to_search - {key}, key))
                hold_size += 1
        for _ in range(min(hold_size, width)):
            item = heappop(hold)
            pre_hold.append(item)
        hold = []
        hold_size = 0
 
    ans_cost, ans_pass, ans_search, ans_id = pre_hold.popleft()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)
 
    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_hold, wf):
    c = store_hold * 1000 / wf[current_id][0]
    for key in order:
        if cost[key][1]  * 10000 / wf[current_id][key] > c: return final_dist
    return 0
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i, j in permutations(range(V), 2):
            if wf[i][j] > wf[i][k] + wf[k][j]:
                wf[i][j] = wf[i][k] + wf[k][j]
                next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = dict()
    for t in range(T): command[t] = -1
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = [0] * V
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, 0, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0
                    root_size = len(root_list)

            if heading in order:
                order -= {heading}
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                for j in range(root_pointer, root_size - 1):
                    if cost[root_list[j + 1]][0] > 0:
                        final_dist = root_list[j + 1]
                        root_pointer = j + 1
                        if current_id > 0:
                            final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf)
                        break
                else: final_dist = 0

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt
from itertools import permutations

def root_search(order, cost, current_id, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id)) #cost, pass, left, id, time
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id = pre_hold.popleft()
            for key in to_search:
                new_cost =  -1 * pre_cost + wf[pre_id][key] / sqrt(cost[key][1])
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key))
                if len(hold) > 4: trush = heappop(hold)
        while hold:
            item = heappop(hold)
            pre_hold.append(item)
 
    ans_cost, ans_pass, ans_search, ans_id = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)
 
    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_hold, wf):
    c = store_hold * 1000 / wf[current_id][0]
    for key in order:
        if cost[key][1]  * 10000 / wf[current_id][key] > c: return final_dist
    return 0
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i, j in permutations(range(V), 2):
            if wf[i][j] > wf[i][k] + wf[k][j]:
                wf[i][j] = wf[i][k] + wf[k][j]
                next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = dict()
    for t in range(T): command[t] = -1
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = [0] * V
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, 0, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0
                    root_size = len(root_list)

            if heading in order:
                order -= {heading}
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                for j in range(root_pointer, root_size - 1):
                    if cost[root_list[j + 1]][0] > 0:
                        final_dist = root_list[j + 1]
                        root_pointer = j + 1
                        if current_id > 0:
                            final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf)
                        break
                else: final_dist = 0

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt

def root_search(order, cost, current_id, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    hold_num = (3 if len(order) >= 300 else 4)
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    next_search = deque()
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id)) #cost, pass, left, id, time
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id = pre_hold.popleft()
            for key in to_search:
                new_cost =  -1 * pre_cost + wf[pre_id][key] / sqrt(cost[key][1])
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key))
                if len(hold) > hold_num: trush = heappop(hold)
        while hold:
            item = heappop(hold)
            pre_hold.append(item)

    ans_cost, ans_pass, ans_search, ans_id = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)

    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_hold, wf, V):
    d = 0
    c = store_hold /(wf[current_id][0]) ** 2
    for key in order:
        if cost[key][1]  / wf[current_id][key]> c:
            return final_dist
    return 0
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = dict()
    for t in range(T): command[t] = -1
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = [0] * V
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, 0, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0

            if heading in order:
                order -= {heading}
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                final_dist = root_list[root_pointer + 1]
                root_pointer += 1

                if current_id > 0:
                    final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf, V)

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt

def root_search(order, cost, current_id, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    next_search = deque()
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id)) #cost, pass, left, id, time
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id = pre_hold.popleft()
            for key in to_search:
                new_cost =  -1 * pre_cost + wf[pre_id][key] / sqrt(cost[key][1])
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key))
                if len(hold) > 4: trush = heappop(hold)
        while hold:
            item = heappop(hold)
            pre_hold.append(item)

    ans_cost, ans_pass, ans_search, ans_id = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)

    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_cost, wf):
    d = 0
    c = store_cost * (1000/wf[current_id][0])
    for key in order:
        if cost[key][1]  * (10000 / wf[current_id][key])> c:
            return final_dist
    return 0
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = dict()
    for t in range(T): command[t] = -1
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = [0] * V
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, 0, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0

            if heading in order:
                order -= {heading}
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                final_dist = root_list[root_pointer + 1]
                root_pointer += 1

                if current_id > 0:
                    final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf)

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()

Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt

def root_search(order, cost, current_id, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    next_search = deque()
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id)) #cost, pass, left, id, time
    for i in range(type_num):
        for _ in range(len(pre_hold)):
            pre_cost, pre_pass, to_search, pre_id = pre_hold.popleft()
            for key in to_search:
                new_cost =  -1 * pre_cost + wf[pre_id][key] / sqrt(cost[key][1])
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key))
                if len(hold) > 4: trush = heappop(hold)
        for _ in range(len(hold)):
            item = heappop(hold)
            pre_hold.append(item)

    ans_cost, ans_pass, ans_search, ans_id = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)

    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_hold, wf):
    d = 0
    c = (wf[current_id][0] + wf[0][final_dist]) / sqrt(store_hold) 
    if wf[current_id][final_dist] / sqrt(cost[final_dist][1]) > c: return 0
    return final_dist
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = dict()
    for t in range(T): command[t] = -1
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = dict()
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        store_list[i] = 0
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, 0, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0

            if heading in order:
                order -= {heading}
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                final_dist = root_list[root_pointer + 1]
                root_pointer += 1

                if current_id > 0 and cost[final_dist][1] > 0 and store_hold > 0:
                    final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf)

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt

def root_search(order, cost, current_id, wf, V): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    next_search = deque()
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id)) #cost, pass, left, id, time
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id = pre_hold.popleft()
            for key in to_search:
                new_cost =  -1 * pre_cost + wf[pre_id][key] / sqrt(cost[key][1])
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key))
                if len(hold) > 3: trush = heappop(hold)
        while hold:
            item = heappop(hold)
            pre_hold.append(item)

    ans_cost, ans_pass, ans_search, ans_id = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)

    return pass_list

def decide_next_dst(cost, order, current_id, final_dist, store_cost, wf):
    d = 0
    c = wf[current_id][0] / sqrt(store_cost) 
    if wf[current_id][final_dist] / sqrt(cost[final_dist][1]) > c: return 0
    return final_dist
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = [None] * T
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    store_list = [0] * V
    root_list = []
    cost = dict()
    store_time = set()
    for i in range(V): 
        cost[i] = [0, 0]
    store_hold = 0
    
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_list[dst - 1] += 1
            store_time |= {t}
           
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    command[t] = -1
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in order: 
                        cost[key][1] += 0.5 * cost[key][0] + store_list[key]
                        cost[key][0] += store_list[key]
                        store_list[key] = 0
                    stuck_order = set()
                    store_time = set()
                    store_hold = 0
                    root_list = root_search(order, cost, 0, wf, V)
                    #print(root_list)
                    current_id = heading = final_dist = 0
                    root_pointer = 0

            if heading in order:
                order -= {heading}
                driver_hold -= cost[heading][0]
                cost[heading] = [0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                final_dist = root_list[root_pointer + 1]
                root_pointer += 1

                if current_id > 0 and store_hold > 0 and cost[final_dist][1] > 0:
                    final_dist = decide_next_dst(cost, order, current_id, final_dist, store_hold, wf)

                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      

    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt

def root_search(order, driver_time, current_id, wf, V, T): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    next_search = deque()
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id, T)) #cost, pass, left, id, time
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id, pre_time = pre_hold.popleft()
            for key in to_search:
                new_time = pre_time + wf[pre_id][key]
                new_cost = new_time ** 2 -new_time * driver_time[key][0] + driver_time[key][1]
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key, new_time))
                if len(hold) > 2: trush = heappop(hold)
        while hold:
            item = heappop(hold)
            pre_hold.append(item)

    ans_cost, ans_pass, ans_search, ans_id, ans_time = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)
    ans_cost *= -1
    fin_time = ans_time + wf[ans_id][0]

    return pass_list, ans_cost, fin_time

def decide_to_return(order, driver_time, stuck_order, store_time, current_id, T, V, wf, cost_left, fin_time):
    #店舗に戻って荷物を取りに戻るべきかどうかを調べる
    back_time = wf[current_id][0]
    new_time = dict()
    for i in range(V): 
        new_time[i] = [driver_time[i][0] + store_time[i][0], driver_time[i][1] + store_time[i][1], 0]
    new_order = order | stuck_order
    
    back_list, back_cost, back_fin_time = root_search(new_order, new_time, 0, wf, V, T + back_time)

    after_list, after_cost, after_fin_time = root_search(stuck_order, store_time, 0, wf, V, fin_time)
    
    if back_cost < cost_left + after_cost: return True
    else: return False
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = [None] * T
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    driver_time = dict()
    store_time = dict()
    root_list = []
    for i in range(V): #[2t * torderの項、torder ** 2の項, 荷物の個数]
        driver_time[i] = [0, 0, 0]
        store_time[i] = [0, 0, 0]
    store_hold = 0
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_time[dst-1][0] += t
            store_time[dst-1][1] += t ** 2
            store_time[dst-1][2] += 1
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    command[t] = -1
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in stuck_order: 
                        driver_time[key][0] += store_time[key][0]
                        driver_time[key][1] += store_time[key][1]
                        driver_time[key][2] += store_time[key][2]
                        store_time[key] = [0, 0, 0]
                    stuck_order = set()
                    store_hold = 0
                    root_list, final_cost, fin_schedule = root_search(order, driver_time, 0, wf, V, t)
                    #print(root_list)
                    fin_cost = 0
                    current_id = heading = final_dist = 0
                    root_pointer = 0
                    len_root = len(root_list) 

            if heading in order:
                fin_cost += t ** 2 - t * driver_time[heading][0] + driver_time[heading][1] 
                order -= {heading}
                driver_hold -= driver_time[heading][2]
                driver_time[heading] = [0, 0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                while root_pointer < len_root - 2 and root_list[root_pointer + 1] not in order:
                    root_pointer += 1
                if root_pointer == len_root - 2: final_dist = 0
                else:
                    final_dist = root_list[root_pointer + 1]
                    root_pointer += 1
                
                if current_id > 0 and driver_hold < store_hold:
                    if decide_to_return(order, driver_time, stuck_order, store_time, current_id, t, V, wf, final_cost - fin_cost, fin_schedule):
                        final_dist = 0
                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      



    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
from heapq import heapify, heappop, heappush
from math import sqrt

def root_search(order, driver_time, current_id, wf, V, T): #店舗から出るときの探索
    type_num = len(order)
    hold = [] #holdで上位n個のみ保持し、最後に残ったものをpre_holdに移す
    heapify(hold)
    pre_hold = deque() #一段階前の確定した道順
    next_search = deque()
    initial = set()
    initial |= order
    pre_hold.append((0, str(current_id), initial, current_id, T)) #cost, pass, left, id, time
    for i in range(type_num):
        while pre_hold:
            pre_cost, pre_pass, to_search, pre_id, pre_time = pre_hold.popleft()
            for key in to_search:
                new_time = pre_time + wf[pre_id][key]
                new_cost = new_time ** 2 -new_time * driver_time[key][0] + driver_time[key][1]
                new_pass = pre_pass + " " + str(key)
                heappush(hold, (-1 * new_cost, new_pass, to_search - {key}, key, new_time))
                if len(hold) > 2: trush = heappop(hold)
        while hold:
            item = heappop(hold)
            pre_hold.append(item)

    ans_cost, ans_pass, ans_search, ans_id, ans_time = pre_hold.pop()
    pass_list = [int(v) for v in ans_pass.split()]
    pass_list.append(0)
    ans_cost *= -1
    fin_time = ans_time + wf[ans_id][0]

    return pass_list, ans_cost, fin_time

def decide_to_return(order, driver_time, stuck_order, store_time, current_id, T, V, wf, cost_left, fin_time):
    #店舗に戻って荷物を取りに戻るべきかどうかを調べる
    back_time = wf[current_id][0]
    new_time = dict()
    for i in range(V): 
        new_time[i] = [driver_time[i][0] + store_time[i][0], driver_time[i][1] + store_time[i][1], 0]
    new_order = order | stuck_order
    
    back_list, back_cost, back_fin_time = root_search(new_order, new_time, 0, wf, V, T + back_time)

    after_list, after_cost, after_fin_time = root_search(stuck_order, store_time, 0, wf, V, fin_time)
    
    if back_cost < cost_left + after_cost: return True
    else: return False
 
def solve():
    inf = 10000000000
    input = sys.stdin.readline
    #fin = open("sampleinput.txt", "r")
    #input = fin.readline
    
    V, E = map(int, input().split())
    edge = dict()
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        edge[i] = dict()
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            edge[i][j] = (0 if i == j else inf)
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
 
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1][v - 1] = d
        edge[v - 1][u - 1] = d
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d
 
    #全頂点最短経路と目的の頂点に向かうとき次に行くべき頂点の復元
    for k in range(V): 
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k]
 
    T = int(input())
    order = set()
    stuck_order = set()
 
    command = [None] * T
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    driver_hold = 0
    root_pointer = 0
    driver_time = dict()
    store_time = dict()
    root_list = []
    for i in range(V): #[2t * torderの項、torder ** 2の項, 荷物の個数]
        driver_time[i] = [0, 0, 0]
        store_time[i] = [0, 0, 0]
    store_hold = 0
 
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            new_id, dst = map(int, input().split())
            stuck_order |= {dst - 1}
            store_hold += 1
            store_time[dst-1][0] += t
            store_time[dst-1][1] += t ** 2
            store_time[dst-1][2] += 1
 
        if dist_left > 0: #移動中の場合そのまま移動を続ける
            command[t] = heading + 1
            dist_left -= 1
        
        else:
            if heading == 0: #店にいるときの処理
                if store_hold == driver_hold == 0: 
                    command[t] = -1
                    continue
                else:
                    order |= stuck_order
                    driver_hold += store_hold
                    for key in stuck_order: 
                        driver_time[key][0] += store_time[key][0]
                        driver_time[key][1] += store_time[key][1]
                        driver_time[key][2] += store_time[key][2]
                        store_time[key] = [0, 0, 0]
                    stuck_order = set()
                    store_hold = 0
                    root_list, final_cost, fin_schedule = root_search(order, driver_time, 0, wf, V, t)
                    #print(root_list)
                    fin_cost = 0
                    current_id = heading = final_dist = 0
                    root_pointer = 0
                    len_root = len(root_list) 

            if heading in order:
                fin_cost += t ** 2 - t * driver_time[heading][0] + driver_time[heading][1] 
                order -= {heading}
                driver_hold -= driver_time[heading][2]
                driver_time[heading] = [0, 0, 0]
 
            current_id = heading #現在地の更新
            if current_id == final_dist:
                while root_pointer < len_root - 2 and root_list[root_pointer + 1] not in order:
                    root_pointer += 1
                if root_pointer == len_root - 2: final_dist = 0
                else:
                    final_dist = root_list[root_pointer + 1]
                    root_pointer += 1
                
                if current_id > 0:
                    if decide_to_return(order, driver_time, stuck_order, store_time, current_id, t, V, wf, final_cost - fin_cost, fin_schedule):
                        final_dist = 0
                
            heading = next_id[current_id][final_dist]
            dist_left = edge[current_id][heading] - 1
            command[t] = heading + 1
 
    for i in range(T): print(command[i])
    #out = open(str(V) + "-" + str(E) + "-out.txt", "w")
    #for i in range(T):  
        #print(command[i], file = out, end ="\n")
    #out.close      



    return 0

if __name__ == "__main__":
    solve()


Fixed submission:
for i in range(10000): print(-1)

Buggy python submission (verdict: Runtime Error):
import sys
from collections import deque
from heapq import heapify, heappop, heappush

def solve():
    inf = 100000000
    input = sys.stdin.readline
    
    V, E = map(int, input().split())
    edge = [[] for _ in range(V)]
    wf = dict()
    next_id = dict() #iからjに行くときにiの次に訪れる地点
    for i in range(V):
        wf[i] = dict()
        next_id[i] = dict()
        for j in range(V):
            next_id[i][j] = j
            wf[i][j] = (0 if i == j else inf)
    for _ in range(E):
        u, v, d = map(int, input().split())
        edge[u - 1].append((d, v - 1))
        edge[v - 1].append((d, u - 1))
        wf[u - 1][v - 1] = d
        wf[v - 1][u - 1] = d

    for k in range(V):
        for i in range(V):
            for j in range(V):
                if wf[i][j] > wf[i][k] + wf[k][j]:
                    wf[i][j] = wf[i][k] + wf[k][j]
                    next_id[i][j] = next_id[i][k] 

    T = int(input())
    order = set()
    stuck_order = set()

    command = [None] * T
    car_status = -2 #-2なら店、iならiへ向かって移動中
    heading = 0 #次に向かう地点
    dist_left = 0 #次に向かう地点までの残り距離
    final_dist = 0
    for t in range(T):
        N = int(input()) #注文の発生
        if N == 1:
            id, dst = map(int, input().split())
            if car_status == -2: order |= {dst - 1}
            else: stuck_order |= {dst - 1}
        
        if car_status == -2: #店にいるときの処理
            if order == {}: command[t] = -1
            else:
                for k in order:
                    final_dist = k
                    heading = next_id[0][k]
                    dist_left = edge[0][heading][0] - 1
                    car_status = heading
                    command[t] = heading
                    break
        
        else:
            if dist_left > 0:
                command[t] = heading
                dist_left -= 1
            else:
                if heading in order: order -= {heading} #荷物の積み下ろし

                if len(order) > 0: #まだ配達すべき荷物があるとき
                    for k in order:
                        current = heading
                        final_dist = k
                        heading = next_id[current][final_dist]
                        dist_left = edge[current][heading][0] - 1
                        car_status = heading
                        command[t] = heading
                        break
                
                else: #荷物が無いので店に戻る
                    final_dist = 0
                    current = heading
                    heading = next_id[current][final_dist]
                    dist_left = edge[current][heading][0] - 1
                    car_status = heading
                    command[t] = heading

    for t in command: print(t)

    return 0

if __name__ == "__main__":
    solve()

Fixed submission:
for i in range(10000): print(-1)