Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
N, K = map(int, input().split())
import numpy as np
As = list(map(lambda x: int(x)-1, input().split()))

cnt = 1
v = 0
checked = [-1]*N
checked[0] = 0
while True:
    v = As[v]
    if checked[v]!=-1:
        loop = cnt-checked[v]
        road = checked[v]
        break
    cnt += 1
    checked[v] = cnt-1

ite = K if K<=road else road+((K-road)%loop)

v = 0
for i in range(ite):
    v = As[v]

print(v+1)

Fixed submission:
N, K = map(int, input().split())
As = list(map(lambda x: int(x)-1, input().split()))

cnt = 1
v = 0
checked = [-1]*N
checked[0] = 0
while True:
    v = As[v]
    if checked[v]!=-1:
        loop = cnt-checked[v]
        road = checked[v]
        break
    cnt += 1
    checked[v] = cnt-1

ite = K if K<=road else road+((K-road)%loop)

v = 0
for i in range(ite):
    v = As[v]

print(v+1)
Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())
mod = 998244353

def comb(a, b):
    global mod
    l, r = 1, 1
    for i in range(b):
        l = l*(b-i)%mod
        r = r*(a-i)%mod
    return (r*pow(l, mod-2, mod))%mod

ans = 0
for i in range(K+1):
    ans += comb(N-1, i)*M*pow((M-1), (N-1-i), mod)%mod

print(ans%mod)


Fixed submission:
N, M, K = map(int, input().split())
mod = 998244353

l_lis = [1]
r_lis = [1]

l, r = 1, 1
for j in range(K+1):
    l = l*(j+1)%mod
    r = r*(N-j-1)%mod
    l_lis.append(l)
    r_lis.append(r)

def comb(a, b):
    global mod
    l = l_lis[b]
    r = r_lis[b]
    return (r*pow(l, mod-2, mod))%mod
 
ans = 0
for i in range(K+1):
    ans += comb(N-1, i)*M*pow((M-1), (N-1-i), mod)%mod

print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())
mod = 998244353

def comb(a, b):
    global mod
    l, r = 1, 1
    for i in range(b):
        l = l*(b-i)%mod
        r = r*(a-i)%mod
    return (r*pow(l, mod-2, mod))%mod

ans = 0
for i in range(K+1):
    ans += comb(N-1, i)*M*pow((M-1), (N-1-i), mod)%mod

print(ans%mod)


Fixed submission:
N, M, K = map(int, input().split())
mod = 998244353

l_lis = [1]
r_lis = [1]

l, r = 1, 1
for j in range(K+1):
    l = l*(j+1)%mod
    r = r*(N-j-1)%mod
    l_lis.append(l)
    r_lis.append(r)

def comb(a, b):
    global mod
    l = l_lis[b]
    r = r_lis[b]
    return (r*pow(l, mod-2, mod))%mod
 
ans = 0
for i in range(K+1):
    ans += comb(N-1, i)*M*pow((M-1), (N-1-i), mod)%mod

print(ans%mod)
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, A, B, C = mapint()
costs = {'A': A, 'B': B, 'C': C}
old_a, old_b = list(input())

if costs[old_a]==0 and costs[old_b]==0:
    print('No')
    exit()
print('Yes')
for _ in range(N-1):
    nx_a, nx_b = list(input())
    if old_a==nx_a or old_a==nx_b:
        print(old_a)
        costs[old_a] += 1
    else:
        print(old_b)
        costs[old_b] += 1
    old_a, old_b = nx_a, nx_b

if not costs[nx_a]:
    print(nx_a)
else:
    print(nx_b)

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, A, B, C = mapint()
costs = {'A': A, 'B': B, 'C': C}
old_a, old_b = list(input())

if costs[old_a]==0 and costs[old_b]==0:
    print('No')
    exit()

commands = []
for _ in range(N-1):
    nx_a, nx_b = list(input())
    if costs[old_a]==0 and costs[old_b]==0:
        print('No')
        exit()
    elif costs[old_a]==0:
        costs[old_a] += 1
        costs[old_b] -= 1
        commands.append(old_a)
        
    elif costs[old_b]==0:
        costs[old_b] += 1
        costs[old_a] -= 1
        commands.append(old_b)

    else:
        if old_a==nx_a or old_a==nx_b:
            commands.append(old_a)
            costs[old_a] += 1
            costs[old_b] -= 1
        else:
            commands.append(old_b)
            costs[old_b] += 1
            costs[old_a] -= 1
    old_a, old_b = nx_a, nx_b

if costs[old_a]==0 and costs[old_b]==0:
    print('No')
    exit()
elif costs[old_a]==0:
    costs[old_a] += 1
    costs[old_b] -= 1
    commands.append(old_a)
    
else:
    costs[old_b] += 1
    costs[old_a] -= 1
    commands.append(old_b)

print('Yes')
print('\n'.join(commands))
Buggy python submission (verdict: Time Limit Exceeded):
A, B, N = map(int, input().split())

ans = 0
for x in range(1, N+1):
    p = int((A*x)/B) - A*int(x/B)
    if p<ans:
        break
    ans = p

print(ans)

    
    

Fixed submission:
A, B, N = map(int, input().split())
from fractions import gcd

ans = 0

x = min(B-1, N)
p = int((A*x)/B) - A*int(x/B)

ans = p

print(ans)
Buggy python submission (verdict: Runtime Error):
K = int(input())

min_r = 0
max_r = 12

def count(idx, n):
    if idx==0:
        return 1
    if n==0:
        return count(idx-1, 1)+count(idx-1, 0)
    elif n==9:
        return count(idx-1, 9)+count(idx-1, 8)
    else:
        return count(idx-1, n-1)+count(idx-1, n)+count(idx-1, n+1)

lists = []
def count_2(idx, n, list_b):
    lis = list_b[:]
    lis.append(str(n))
    if idx==0:
        lists.append(int(''.join(lis)))
        return 1
    if n==0:
        count_2(idx-1, 1, lis)
        count_2(idx-1, 0, lis)
    elif n==9:
        count_2(idx-1, 9, lis)
        count_2(idx-1, 8, lis)
    else:
        count_2(idx-1, n-1, lis)
        count_2(idx-1, n, lis)
        count_2(idx-1, n+1, lis)

d = 0
now = 0
while 1:
    p = sum([count(d, i) for i in range(1, 10)])
    now += p
    if now>K:
        now -= p
        break
    d += 1

sump = 0
for i in range(1, 10):
    sump_old = sump
    sump += count(d, i)
    if sump+now>K:
        break
count_2(d, i, [])
print(lists[K-now-sump_old+1])

Fixed submission:
K = int(input())

def count(idx, n):
    if idx==0:
        return 1
    if n==0:
        return count(idx-1, 1)+count(idx-1, 0)
    elif n==9:
        return count(idx-1, 9)+count(idx-1, 8)
    else:
        return count(idx-1, n-1)+count(idx-1, n)+count(idx-1, n+1)

lists = []
def count_2(idx, n, list_b):
    lis = list_b[:]
    lis.append(str(n))
    if idx==0:
        lists.append(int(''.join(lis)))
        return 1
    if n==0:
        count_2(idx-1, 1, lis)
        count_2(idx-1, 0, lis)
    elif n==9:
        count_2(idx-1, 9, lis)
        count_2(idx-1, 8, lis)
    else:
        count_2(idx-1, n-1, lis)
        count_2(idx-1, n, lis)
        count_2(idx-1, n+1, lis)

d = 0
now = 0
while 1:
    p = sum([count(d, i) for i in range(1, 10)])
    now += p
    if now>K:
        now -= p
        break
    d += 1

sump = 0
for i in range(1, 10):
    sump_old = sump
    sump += count(d, i)
    if sump+now>=K:
        break
count_2(d, i, [])
lists.sort()
if K<10:
    print(K)
else:
    print(lists[K-now-sump_old-1])
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

from sympy import divisors
N = int(input())
ans = len(divisors(N-1))-1
lis = divisors(N)
for n in lis:
    G = N
    if n==1:
        continue
    while G%n==0:
        G //= n
    if G%n==1:
        ans += 1
print(ans)

Fixed submission:
from math import sqrt
N = int(input())
ans = 0
divisors = []

for i in range(2, int(sqrt(N))+1):
    if N%i==0:
        divisors.append(i)
        divisors.append(N//i)

for d in set(divisors):
    i = 1
    while N%(d**i)==0:
        i += 1
    n = N//(d**(i-1))
    if n%d==1:
        ans+=1

for i in range(2, int(sqrt(N))+1):
    if (N-1)%i==0:
        if i**2!=N-1:
            ans += 2
        else:
            ans += 1
if N==2:
    print(1)
else:
    print(ans+2)
Buggy python submission (verdict: Time Limit Exceeded):
N, X, Y = map(int, input().split())
X -= 1
Y -= 1
dis_lis = [0]*N
for i in range(N-1):
    for j in range(i+1, N):
        if abs(i-j)==1:
            dis_lis[1] += 1
        else:
            min1 = abs(i-j)
            min2 = abs(i-X)+abs(j-Y)+1
            min3 = abs(i-Y)+abs(j-X)+1
            dis_lis[min(min1, min2, min3)] += 1
for i in range(1, N):
    print(dis_lis[i])

Fixed submission:
from collections import deque
from collections import Counter
N, X, Y = map(int, input().split())
X -= 1
Y -= 1
dis_lis = deque()
for i in range(N-1):
    for j in range(i+1, N):
        if abs(i-j)==1:
            dis_lis.append(1)
        else:
            min1 = abs(i-j)
            min2 = abs(i-X)+abs(j-Y)+1
            min3 = abs(i-Y)+abs(j-X)+1
            dis_lis.append(min(min1, min2, min3))
c = Counter(dis_lis)
for i in range(1, N):
    print(c[i])

Buggy python submission (verdict: Time Limit Exceeded):
N, X, Y = map(int, input().split())
X -= 1
Y -= 1
dis_lis = {i:0 for i in range(1, N+1)}
for i in range(N):
    for j in range(N):
        if i==j: continue
        if abs(i-j)==1:
            dis_lis[1] += 1
        else:
            min1 = abs(i-j)
            min2 = abs(i-X)+abs(j-Y)+1
            min3 = abs(i-Y)+abs(j-X)+1
            dis_lis[min(min1, min2, min3)] += 1
for i in range(1, N):
    print(dis_lis[i]//2)

Fixed submission:
from collections import deque
from collections import Counter
N, X, Y = map(int, input().split())
X -= 1
Y -= 1
dis_lis = deque()
for i in range(N-1):
    for j in range(i+1, N):
        if abs(i-j)==1:
            dis_lis.append(1)
        else:
            min1 = abs(i-j)
            min2 = abs(i-X)+abs(j-Y)+1
            min3 = abs(i-Y)+abs(j-X)+1
            dis_lis.append(min(min1, min2, min3))
c = Counter(dis_lis)
for i in range(1, N):
    print(c[i])
Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
N = int(input())
As = list(map(int, input().split()))
for i in range(N):
  Bs = As[:]
  Bs.pop(i)
  c = Counter(Bs)
  ans = 0
  for con in c.most_common():
    if con[1]<2:
      break
    ans += (con[1]*(con[1]-1)/2)
  print(int(ans))

Fixed submission:
from collections import Counter
N = int(input())
As = list(map(int, input().split()))
c = Counter(As)
ans = 0
for con in c.most_common():
  if con[1]<2:
    break
  ans += (con[1]*(con[1]-1)/2)
for i in range(N):
  print(int(ans-c[As[i]]+1))
Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())
L = list(map(int, input().split()))
S = []
for i, x in enumerate(L):
  for y in L[i+1:]:
    S.append(x*y)
print(sorted(S)[K-1])

Fixed submission:
import numpy as np
N, K = map(int, input().split())
L = np.array(list(map(int, input().split())))

L = np.sort(L)
pos = L[0<L]
neg = L[0>L]
zero = len(L[L==0])

def f(x):
  tmp = 0
  if x>=0:
    tmp += zero*N
  tmp += np.searchsorted(L, x//pos, side='right').sum()
  tmp += (N - np.searchsorted(L, -(-x//neg), side='left')).sum()
  tmp -= np.count_nonzero(L*L<=x)
  return tmp//2

l, r = -10**18, 10**18
while l<r-1:
  m = (l+r)//2
  count = f(m)
  if count >= K:
    r = m
  else:
    l = m

print(r)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())
L = list(map(int, input().split()))
S = []
for i, x in enumerate(L):
  for y in L[i+1:]:
    S.append(x*y)
print(sorted(S)[K-1])

Fixed submission:
import numpy as np
N, K = map(int, input().split())
L = np.array(list(map(int, input().split())))

L = np.sort(L)
pos = L[0<L]
neg = L[0>L]
zero = len(L[L==0])

def f(x):
  tmp = 0
  if x>=0:
    tmp += zero*N
  tmp += np.searchsorted(L, x//pos, side='right').sum()
  tmp += (N - np.searchsorted(L, -(-x//neg), side='left')).sum()
  tmp -= np.count_nonzero(L*L<=x)
  return tmp//2

l, r = -10**18, 10**18
while l<r-1:
  m = (l+r)//2
  count = f(m)
  if count >= K:
    r = m
  else:
    l = m

print(r)
Buggy python submission (verdict: Runtime Error):
MOD = 10**9+7
r1,c1,r2,c2 = map(int,input().split())
 
size = 1000000*2
f_list = [1]*(size)
for i in range(1,size):
    f_list[i] = (f_list[i-1]*i)%MOD

def func(r,c):
    return (f_list[r+c]*pow(f_list[r],MOD-2,MOD)*pow(f_list[c],MOD-2,MOD))
 
ans = func(r2+1,c2+1)-1
ans += func(r1,c1)-1
ans -= func(r2+1,c1)-1
ans -= func(r1,c2+1)-1
print(ans%MOD)

Fixed submission:
MOD = 10**9+7
r1,c1,r2,c2 = map(int,input().split())
 
size = 1010000*2
f_list = [1]*(size)
for i in range(1,size):
    f_list[i] = (f_list[i-1]*i)%MOD

def func(r,c):
    return (f_list[r+c]*pow(f_list[r],MOD-2,MOD)*pow(f_list[c],MOD-2,MOD))
 
ans = func(r2+1,c2+1)-1
ans += func(r1,c1)-1
ans -= func(r2+1,c1)-1
ans -= func(r1,c2+1)-1
print(ans%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
r1, c1, r2, c2 = map(int, input().split())
mod = 10**9+7

import numpy as np
graph = [[1]*(r2+1) for _ in range(c2+1)]
graph = np.array(graph)

for i in range(1, c2+1):
    graph[i][1:] = (graph[0][:-1] + np.cumsum(graph[i-1][1:]))%mod

cum_graph = (np.cumsum(np.cumsum(graph, axis=0), axis=1))%mod

print((cum_graph[c2][r2]-cum_graph[c1-1][r2]-cum_graph[c2][r1-1]+cum_graph[c1-1][r1-1])%mod)
    


Fixed submission:
MOD = 10**9+7
r1,c1,r2,c2 = map(int,input().split())
 
size = 1010000*2
f_list = [1]*(size)
for i in range(1,size):
    f_list[i] = (f_list[i-1]*i)%MOD

def func(r,c):
    return (f_list[r+c]*pow(f_list[r],MOD-2,MOD)*pow(f_list[c],MOD-2,MOD))
 
ans = func(r2+1,c2+1)-1
ans += func(r1,c1)-1
ans -= func(r2+1,c1)-1
ans -= func(r1,c2+1)-1
print(ans%MOD)
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

H, W, K = mapint()
cake = [list(str(input())) for _ in range(H)]
ans = [[0]*W for _ in range(H)]
cnt = 0
unchecked_row = [0]*H
for h in range(H):
    row = cake[h]
    if '#' in row:
        cnt += 1
        first = 1
        for i, r in enumerate(row):
            if r=='.':
                ans[h][i] = str(cnt)
            else:
                if first:
                    first=0
                    ans[h][i] = str(cnt)
                    continue
                cnt += 1
                ans[h][i] = str(cnt)
    else:
        unchecked_row[h] = 1
for i, unchecked in enumerate(unchecked_row):
    if unchecked:
        for j in range(1, H):
            if i-j>=0 and not unchecked_row[i-j]:
                ans[i] = ans[i-j][:]
                break
            elif i+j<=H and not unchecked_row[i+j]:
                ans[i] = ans[i+j][:]
                break
for h in range(H):
    print(' '.join(ans[h]))

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

H, W, K = mapint()
cake = [list(str(input())) for _ in range(H)]
ans = [['0']*W for _ in range(H)]
cnt = 0
unchecked_row = [0]*H
for h in range(H):
    row = cake[h]
    if '#' in row:
        cnt += 1
        first = 1
        for i, r in enumerate(row):
            if r=='.':
                ans[h][i] = str(cnt)
            else:
                if first:
                    first=0
                    ans[h][i] = str(cnt)
                    continue
                cnt += 1
                ans[h][i] = str(cnt)
    else:
        unchecked_row[h] = 1
for i, unchecked in enumerate(unchecked_row):
    if unchecked:
        for j in range(1, H):
            if i-j>=0 and not unchecked_row[i-j]:
                ans[i] = ans[i-j][:]
                unchecked_row[i] = 0
                break
            elif i+j<=H and not unchecked_row[i+j]:
                ans[i] = ans[i+j][:]
                unchecked_row[i] = 0
                break
for h in range(H):
    print(' '.join(ans[h]))
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N = int(input())
Ds = list(mapint())

ans = 0
for i in range(N-1):
    for j in range(i+1, N):
        aNS += Ds[i]*Ds[j]

print(ans)

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N = int(input())
Ds = list(mapint())

ans = 0
for i in range(N-1):
    for j in range(i+1, N):
        ans += Ds[i]*Ds[j]

print(ans)
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

S = list(input())
K = int(input())
leng = len(S)
if len(set(S))==1:
    print(S*K//2)
    exit()
if S[0]!=S[-1] or K==1:
    last = S[0]
    cnt = 0
    for s in S[1:]:
        if s==last:
            cnt += 1
            last = '.'
        else:
            last = s
    print(cnt*K)
else:
    S += ['.']
    cnt = 1
    lis = []
    last = S[0]
    for s in S[1:]:
        if s==last:
            cnt += 1
        else:
            lis.append(cnt)
            last = s
            cnt = 1
    first = lis.pop(0)
    end = lis.pop()
    others = sum([i//2 for i in lis])
    ans = first//2 + others*K + (first+end)//2*(K-1)+end//2
    print(ans)


Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

S = list(input())
K = int(input())
leng = len(S)
if len(set(S))==1:
    print(K*leng//2)
    exit()
if S[0]!=S[-1] or K==1:
    last = S[0]
    cnt = 0
    for s in S[1:]:
        if s==last:
            cnt += 1
            last = '.'
        else:
            last = s
    print(cnt*K)
else:
    S += ['.']
    cnt = 1
    lis = []
    last = S[0]
    for s in S[1:]:
        if s==last:
            cnt += 1
        else:
            lis.append(cnt)
            last = s
            cnt = 1
    first = lis.pop(0)
    end = lis.pop()
    others = sum([i//2 for i in lis])
    ans = first//2 + others*K + (first+end)//2*(K-1)+end//2
    print(ans)
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

from math import ceil
N, K = mapint()
S = list(str(input()))

old = S[0]
lis = []
cnt = 1
for i in range(1, N):
    s = S[i]
    if s!=old:
        lis.append(cnt)
        old = s
        cnt = 1
    else:
        cnt += 1
lis.append(cnt)
for l in range(K):
    if len(lis)>=3:
        l1 = lis.pop()
        l2 = lis.pop()
        lis[-1] += (l1+l2)
    else:
        l1 = lis.pop()
        lis[-1] += l1
        break

ans = sum([i-1 for i in lis])
print(ans)

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

from math import ceil
N, K = mapint()
S = list(str(input()))

old = S[0]
lis = []
cnt = 1
for i in range(1, N):
    s = S[i]
    if s!=old:
        lis.append(cnt)
        old = s
        cnt = 1
    else:
        cnt += 1
lis.append(cnt)
for l in range(K):
    if len(lis)>=3:
        l1 = lis.pop()
        l2 = lis.pop()
        lis[-1] += (l1+l2)
    elif len(lis)>=2:
        l1 = lis.pop()
        lis[-1] += l1
        break
    else:
        break

ans = sum([i-1 for i in lis])
print(ans)
Buggy python submission (verdict: Runtime Error):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

A, B = mapint()
print(mas(A+B, A-B, A*B))

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

A, B = mapint()
print(max(A+B, A-B, A*B))
Buggy python submission (verdict: Time Limit Exceeded):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)
from bisect import bisect_right

N, M = mapint()
AB = []
for _ in range(N):
    a, b = mapint()
    AB.append((a, -b))
AB.sort()

days = [0]*M
for a, b in AB:
    a -= 1
    if a>=M:
        continue
    if days[a]==0:
        days[a] = b
    else:
        idx = bisect_right(days[a:], b)
        if a+idx>=M:
            continue
        days[a+idx:] = [b]+days[a+idx:-1]

print(-sum(days[::-1]))

Fixed submission:
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)
from bisect import bisect_right

N, M = mapint()

from heapq import heappop, heappush
days = [[] for _ in range(M)]
for _ in range(N):
    a, b = mapint()
    if a>M:
        continue
    days[a-1].append(-b)

queue = []

ans = 0
for i in range(M):
    lis = days[i]
    for b in lis:
        heappush(queue, b)
    if queue:
        ans += heappop(queue)

print(-ans)
Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
dp = [[0]*(13) for _ in range(N+1)]
dp[0][0] = 1
mod = 10**9+7
for n in range(N):
    s = S[n]
    if s!='?':
        s = int(s)*pow(10, (N-n-1), 13)%13
        for i in range(13):
            idx = (s+i)%13
            dp[n+1][idx] = dp[n][i]%mod
    else:
        for i in range(10):
            s = i*pow(10, (N-n-1), 13)%13
            for j in range(13):
                idx = (s+j)%13
                dp[n+1][idx] += dp[n][j]%mod

print(dp[-1][5]%mod)

Fixed submission:
S = input()
N = len(S)
dp = [[0]*(13) for _ in range(N+1)]
dp[0][0] = 1
mod = 10**9+7
for n in range(N):
    s = S[n]
    if s!='?':
        s = int(s)*pow(10, (N-n-1), 13)%13
        for i in range(13):
            idx = (s+i)%13
            dp[n+1][idx] = dp[n][i]%mod
    else:
        for i in range(10):
            s = i*pow(10, (N-n-1), 13)%13
            for j in range(13):
                idx = (s+j)%13
                dp[n+1][idx] += dp[n][j]%mod

print(dp[-1][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
dp = [[0]*(13) for _ in range(N+1)]
dp[0][0] = 1
mod = 10**9+7
for n in range(N):
    s = S[n]
    if s!='?':
        s = int(s)*(10**(N-n-1))%13
        for i in range(13):
            idx = (s+i)%13
            dp[n+1][idx] = dp[n][i]%mod
    else:
        for i in range(10):
            s = i*(10**(N-n-1))%13
            for j in range(13):
                idx = (s+j)%13
                dp[n+1][idx] += dp[n][j]%mod

print(dp[-1][5]%mod)

Fixed submission:
S = input()
N = len(S)
dp = [[0]*(13) for _ in range(N+1)]
dp[0][0] = 1
mod = 10**9+7
for n in range(N):
    s = S[n]
    if s!='?':
        s = int(s)*pow(10, (N-n-1), 13)%13
        for i in range(13):
            idx = (s+i)%13
            dp[n+1][idx] = dp[n][i]%mod
    else:
        for i in range(10):
            s = i*pow(10, (N-n-1), 13)%13
            for j in range(13):
                idx = (s+j)%13
                dp[n+1][idx] += dp[n][j]%mod

print(dp[-1][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
dp = [[0]*(13) for _ in range(N+1)]
dp[0][0] = 1
mod = 10**9+7
for n in range(N):
    s = S[n]
    if s!='?':
        s = int(s)*(10**(N-n-1))%13
        for i in range(13):
            idx = (s+i)%13
            dp[n+1][idx] = dp[n][i]%mod
    else:
        for i in range(10):
            s = i*(10**(N-n-1))%13
            for j in range(13):
                idx = (s+j)%13
                dp[n+1][idx] += dp[n][j]%mod

print(dp[-1][5]%mod)

Fixed submission:
S = input()
N = len(S)
dp = [[0]*(13) for _ in range(N+1)]
dp[0][0] = 1
mod = 10**9+7
for n in range(N):
    s = S[n]
    if s!='?':
        s = int(s)*pow(10, (N-n-1), 13)%13
        for i in range(13):
            idx = (s+i)%13
            dp[n+1][idx] = dp[n][i]%mod
    else:
        for i in range(10):
            s = i*pow(10, (N-n-1), 13)%13
            for j in range(13):
                idx = (s+j)%13
                dp[n+1][idx] += dp[n][j]%mod

print(dp[-1][5]%mod)