Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
li_a = list(map(int, input().split()))
if k == 1:
    for i in range(1, n):
        if li_a[i] > li_a[i-1]:
            print('Yes')
        else:
            print('No')
else:
    li = []
    tmp = 1
    for i in range(k):
        tmp *= li_a[i]
    li.append(tmp)
    for i in range(k, n):
        tmp = tmp // li_a[i-k]
        tmp  *= li_a[i]
        li.append(tmp)
    for i in range(1, n-k+1):
        if li[i] > li[i-1]:
            print('Yes')
        else:
            print('No')

Fixed submission:
n, k = map(int, input().split())
li_a = list(map(int, input().split()))
if k == 1:
    for i in range(1, n):
        if li_a[i] > li_a[i-1]:
            print('Yes')
        else:
            print('No')
else:
    for i in range(k, n):
        if li_a[i-k] < li_a[i]:
            print('Yes')
        else:
            print('No')
Buggy python submission (verdict: Time Limit Exceeded):
k = int(input())
s = input()
n = len(s)
#nCk(mod p)を求める
def comb(n, k, p):
    if n<0 or k<0 or n<k:
        return 0
    if n==0 or k==0:
        return 1
    a, b, c = 1, 1, 1
    for i in range(1, n+1):
        a = (a*i)%p
    for i in range(1, k+1):
        b = (b*i)%p
    for i in range(1, n-k+1):
        c = (c*i)%p
    return a*pow(b, p-2, p)*pow(c, p-2, p)%p
mod = 10**9+7
ans = 0
for i in range(k+1):
    pls = pow(25, i, mod)
    pls *= pow(26,k-i, mod)
    pls %= mod
    pls *= comb(i+n-1, i, mod)
    ans += pls
    ans %= mod
print(ans%mod)

Fixed submission:
MAX = 10**6 * 3
MOD = 10**9+7
fac = [0] * MAX
finv = [0] * MAX
inv = [0] * MAX
#前処理 逆元テーブルを作る
def COMinit():
    fac[0] = 1
    fac[1] = 1
    finv[0] = 1
    finv[1] = 1
    inv[1] = 1
    for i in range(2, MAX):
        fac[i] = fac[i-1] * i % MOD
        inv[i] = MOD - inv[MOD%i] * (MOD//i)%MOD
        finv[i] = finv[i-1] * inv[i] % MOD
#実行
def COM(n, k):
    if n  < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD
k = int(input())
s = input()
n = len(s)
COMinit()
ans = 0
for i in range(k+1):
    pls = pow(25, i, MOD)
    pls *= pow(26,k-i, MOD)
    pls %= MOD
    pls *= COM(i+n-1, i)
    ans += pls
    ans %= MOD
print(ans%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
k = int(input())
s = input()
n = len(s)
#nCk(mod p)を求める
def comb(n, k, p):
    if n<0 or k<0 or n<k:
        return 0
    if n==0 or k==0:
        return 1
    a, b, c = 1, 1, 1
    for i in range(1, n+1):
        a = (a*i)%p
    for i in range(1, k+1):
        b = (b*i)%p
    for i in range(1, n-k+1):
        c = (c*i)%p
    return a*pow(b, p-2, p)*pow(c, p-2, p)%p
mod = 10**9+7
ans = 0
for i in range(k+1):
    pls = pow(25, i, mod)
    pls *= pow(26,k-i, mod)
    pls *= comb(i+n-1, i, mod)
    ans += pls
print(ans%mod)

Fixed submission:
MAX = 10**6 * 3
MOD = 10**9+7
fac = [0] * MAX
finv = [0] * MAX
inv = [0] * MAX
#前処理 逆元テーブルを作る
def COMinit():
    fac[0] = 1
    fac[1] = 1
    finv[0] = 1
    finv[1] = 1
    inv[1] = 1
    for i in range(2, MAX):
        fac[i] = fac[i-1] * i % MOD
        inv[i] = MOD - inv[MOD%i] * (MOD//i)%MOD
        finv[i] = finv[i-1] * inv[i] % MOD
#実行
def COM(n, k):
    if n  < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD
k = int(input())
s = input()
n = len(s)
COMinit()
ans = 0
for i in range(k+1):
    pls = pow(25, i, MOD)
    pls *= pow(26,k-i, MOD)
    pls %= MOD
    pls *= COM(i+n-1, i)
    ans += pls
    ans %= MOD
print(ans%MOD)
Buggy python submission (verdict: Runtime Error):
import sys
read = sys.stdin.readline
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import numpy as np
MOD = 10 ** 9 + 7

N, K = map(int, read().split())

k = np.arange(K, N + 2, dtype=np.int64)
low = (k - 1) * k // 2
high = N * k - low
cnt = high - low + 1
print(cnt.sum() % MOD)


Fixed submission:
N, K = map(int, input().split())
S1 = 0
S2 = 0
for k in range(1, N+1):
    S1 += k*N - k*(k-1) +1
    S1 %= 10**9 + 7
for k in range(1, K):
    S2 += k*N - k*(k-1) +1
    S2 %= 10**9 + 7
    
S = S1 - S2 + 1
S %= 10**9 +7

print(S)

Buggy python submission (verdict: Runtime Error):
import sys
read = sys.stdin.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import numpy as np
MOD = 10 ** 9 + 7

N, K = map(int, read().split())

k = np.arange(K, N + 2, dtype=np.int64)
low = (k - 1) * k // 2
high = N * k - low
cnt = high - low + 1
print(cnt.sum() % MOD)


Fixed submission:
N, K = map(int, input().split())
S1 = 0
S2 = 0
for k in range(1, N+1):
    S1 += k*N - k*(k-1) +1
    S1 %= 10**9 + 7
for k in range(1, K):
    S2 += k*N - k*(k-1) +1
    S2 %= 10**9 + 7
    
S = S1 - S2 + 1
S %= 10**9 +7

print(S)

Buggy python submission (verdict: Runtime Error):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import numpy as np
MOD = 10 ** 9 + 7

N, K = map(int, read().split())

k = np.arange(K, N + 2, dtype=np.int64)
low = (k - 1) * k // 2
high = N * k - low
cnt = high - low + 1
print(cnt.sum() % MOD)


Fixed submission:
N, K = map(int, input().split())
S1 = 0
S2 = 0
for k in range(1, N+1):
    S1 += k*N - k*(k-1) +1
    S1 %= 10**9 + 7
for k in range(1, K):
    S2 += k*N - k*(k-1) +1
    S2 %= 10**9 + 7
    
S = S1 - S2 + 1
S %= 10**9 +7

print(S)
Buggy python submission (verdict: Time Limit Exceeded):
x = int(input())
from math import gcd
c = 0
for i in range(1,x+1):
    for j in range(1, x+1):
        for k in range(1, x+1):
            a = gcd(i, j)
            b = gcd(a, k)
            c += b
print(c)

Fixed submission:
x = int(input())
from math import gcd
c = 0
for i in range(1,x+1):
    for j in range(1, x+1):
        for k in range(1, x+1):
            a = gcd(i, j)
            b = gcd(a, k)
            c += b
print(c)
Buggy python submission (verdict: Runtime Error):
#n桁のるんるん数のrisutoを求める
import sys

sys.setrecursionlimit(10**9)
def runrun(n):
    if n == 1:
        return [['1','2','3','4','5','6','7','8','9']]
    else:
        li = runrun(n-1)
        li2 = []
        for i in range(len(li[n-2])):
            p = int(li[n-2][i][-1])
            if p == 0:
                li2.append(li[n-2][i]+'0')
                li2.append(li[n-2][i]+'1')
            elif p == 9:
                li2.append(li[n-2][i]+str(8))
                li2.append(li[n-2][i]+'9')
            else:
                li2.append(li[n-2][i]+str(p-1))
                li2.append(li[n-2][i]+str(p))
                li2.append(li[n-2][i]+str(p+1))
        li2 =[li2]
        li.extend(li2)
        return li
    


x = int(input())
t = True
k=1
b = 0
while t:
    
    a = runrun(k)
    #k桁までに何個るんるん数があるか数えるもの
    for i in range(len(a)):
        b+=(len(a[i])-1)
        #k桁ということが確定したあと以下の処理を行う
    if x <= b:
        t = False
        if k == 1:
            print(x)
        else:
            tmp = runrun(k-1)
            c = 0
            for i in range(len(tmp)):
                c+=len(tmp[i])
            s = a[k-1][x-c-1]
            print(int(s))
    else:
        b += 1
        k += 1
        

Fixed submission:
#n桁のるんるん数のrisutoを求める
import sys

sys.setrecursionlimit(10**9)

def runrun(n):
    if n == 1:
        return [['1','2','3','4','5','6','7','8','9']]
    else:
        li = runrun(n-1)
        li2 = []
        for i in range(len(li[n-2])):
            p = int(li[n-2][i][-1])
            if p == 0:
                li2.append(li[n-2][i]+'0')
                li2.append(li[n-2][i]+'1')
            elif p == 9:
                li2.append(li[n-2][i]+str(8))
                li2.append(li[n-2][i]+'9')
            else:
                li2.append(li[n-2][i]+str(p-1))
                li2.append(li[n-2][i]+str(p))
                li2.append(li[n-2][i]+str(p+1))
        li2 =[li2]
        li.extend(li2)
        return li
    


x = int(input())
t = True
k=1
b = 0
while t:
    a = runrun(k)
    b = 0
    #k桁までに何個るんるん数があるか数えるもの
    for i in range(len(a)):
        b+=(len(a[i]))
        #k桁ということが確定したあと以下の処理を行う
    if x <= b:
        t = False
        if k == 1:
            print(x)
        else:
            tmp = runrun(k-1)
            c = 0
#まずk-1桁までのるんるん数の数を数える
            for i in range(len(tmp)):
                c += (len(tmp[i]))
            s = a[k-1][x-c-1]
            print(int(s))
    else:
        k += 1
Buggy python submission (verdict: Runtime Error):
x,y,a,b,c = map(int, input().split())
li_p = list(map(int, input().split()))
li_q = list(map(int, input().split()))
li_r = list(map(int, input().split()))
li_p.sort(reverse=True)
li_q.sort(reverse=True)
li_r.sort(reverse=True)
p,q = [],[]
for i in range(x):
  r.append(li_p[i])
for i in range(y):
  r.append(li_q[i])
for i in range(c):
  r.append(li_r[i])
r.sort(reverse=True)
print(sum(r[:x+y]))

Fixed submission:
x,y,a,b,c = map(int, input().split())
li_p = list(map(int, input().split()))
li_q = list(map(int, input().split()))
li_r = list(map(int, input().split()))
li_p.sort(reverse=True)
li_q.sort(reverse=True)
li_r.sort(reverse=True)
r = []
for i in range(x):
  r.append(li_p[i])
for i in range(y):
  r.append(li_q[i])
for i in range(c):
  r.append(li_r[i])
r.sort(reverse=True)
print(sum(r[:x+y]))
Buggy python submission (verdict: Runtime Error):
h, w = map(int, input().split())
g = [[0] * w for _ in range(h)]#白が1、黒が０
for i in range(h):
    s = list(input())
    for j in range(w):
        if s[j] == '.':
            g[i][j] = 1
INF = 10**9
dp = [[INF] * w for _ in range(h)]
if g[0][0] == 0:
    dp[0][0] = 1
else:
    dp[0][0] = 0

for i in range(h):
    for j in range(w):
        for dx, dy in ((1, 0), (0, 1)):
            nx = j + dx
            ny = i + dy
            if nx >= h or ny >= w:
                continue
            add = 0
            if g[ny][nx] == 0 and g[i][j]  == 1:
                add = 1
            dp[ny][nx] = min(dp[ny][nx], dp[i][j] + add)
            
print(dp[h-1][w-1])




Fixed submission:
h, w = map(int, input().split())
g = [[0] * w for _ in range(h)]#白が1、黒が０
for i in range(h):
    s = list(input())
    for j in range(w):
        if s[j] == '.':
            g[i][j] = 1
INF = 10**9
dp = [[INF] * w for _ in range(h)]
if g[0][0] == 0:
    dp[0][0] = 1
else:
    dp[0][0] = 0

for i in range(h):
    for j in range(w):
        for dx, dy in ((1, 0), (0, 1)):
            nx = j + dx
            ny = i + dy
            if ny >= h or nx >= w:
                continue
            add = 0
            if g[ny][nx] == 0 and g[i][j]  == 1:
                add = 1
            dp[ny][nx] = min(dp[ny][nx], dp[i][j] + add)
            
print(dp[h-1][w-1])
Buggy python submission (verdict: Runtime Error):
N = int(input())
R = int(input())

if N > 9:
  print(R)
else:
  R += 100*(10-N)
  print(R)

Fixed submission:
N,R = map(int,input().split())

if N > 9:
  print(R)
else:
  R += 100*(10-N)
  print(R)
Buggy python submission (verdict: Time Limit Exceeded):

N,a,b = map(int,input().split())
Sum = pow(2, N, 10**9+7)-1
MOD = 10**9 + 7
def comb(n,k, mod):
    m = 1#分子
    l = 1#bunnbo
    for i in range(k):
        m *= (n-i)
        l *= (i + 1)
        m %= mod
    return m * pow(l, mod-2, mod) % mod

Sum = pow(2, N, 10**9+7) -1 - comb(N, a, MOD) - comb(N, b, MOD)
Sum = Sum % (10**9+7)
print(Sum)

Fixed submission:

N,a,b = map(int,input().split())
MOD = 10**9 + 7
def comb(n,k, mod):
    m = 1#分子
    l = 1#bunnbo
    for i in range(k):
        m *= n - i
        l *= (i + 1)
        m %= mod
        l %= mod
    return m * pow(l, mod-2, mod) % mod

Sum = pow(2, N, 10**9+7) -1 - comb(N, a, MOD) - comb(N, b, MOD)
Sum = Sum % (10**9+7)
print(Sum)
Buggy python submission (verdict: Time Limit Exceeded):
x = int(input())
li = list(map(int,input().split()))
for i in range(len(li)):
    for k in range(len(li)):
        if i > k:
            if li[i] == li[k]:
                print('NO')
                exit()
    if i == len(li) -1:
        print('YES')

Fixed submission:
import sys
input = sys.stdin.readline
x = int(input())
from collections import defaultdict
A=[int(i) for i in input().split()]
dd=defaultdict(int)
for a in A:
    dd[a]+=1
for i in dd:
    if dd[i] > 1:
        print('NO')
        exit()
print('YES')
Buggy python submission (verdict: Runtime Error):
x,y = map(int,input().split())
li = list(map(int,input().split()))
from collections import deque
l = []
for i in range(len(li)):
    l.append((1+ li[i])/2)
from itertools import accumulate
a = list(accumulate(l))
M = a[y-1]
for i range(len(a)-y):
    m = a[i+y] - a[i]
    if m > M:
        M = m
print(M)

Fixed submission:
x,y = map(int,input().split())
li = list(map(int,input().split()))
from collections import deque
l = []
for i in range(len(li)):
    l.append((1+ li[i])/2)
from itertools import accumulate
a = list(accumulate(l))
M = a[y-1]
for i in range(len(a)-y):
    m = a[i+y] - a[i]
    if m > M:
        M = m
print(M)

Buggy python submission (verdict: Time Limit Exceeded):
x,y = map(int,input().split())
li = list(map(int,input().split()))
from collections import deque
l = []
for i in range(len(li)):
    l.append((1+ li[i])/2)
M = 0

for i in range(len(l)-y+1):
    ll = l[i:i+y]
    m=0
    for k in range(y):
        m += ll[k]
    if m > M:
            M = m
print(M)

Fixed submission:
x,y = map(int,input().split())
li = list(map(int,input().split()))
from collections import deque
l = []
for i in range(len(li)):
    l.append((1+ li[i])/2)
from itertools import accumulate
a = list(accumulate(l))
M = a[y-1]
for i in range(len(a)-y):
    m = a[i+y] - a[i]
    if m > M:
        M = m
print(M)
Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline

x = int(input())
li = list(map(int, input().split()))

a = 0 # カウントする

for i in range(len(li)):
    c = 0
    j = 0
    while i >= j:
        if li[i] <=  li[j]:
            c += 1
            if c == i+1:
                a += 1
        j+=1
print(a)

Fixed submission:

x = int(input())
li = list(map(int, input().split()))

a = 0
Min = li[0]
for i in range(len(li)):
    if li[i] <= Min:
        Min = li[i]
        a += 1
print(a)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline

x = int(input())
li = list(map(int, input().split()))

a = 0 # カウントする

for i in range(len(li)):
    c = 0
    j = 0
    while i >= j:
        if li[i] <=  li[j]:
            c += 1
            if c == i+1:
                a += 1
        j+=1
print(a)

Fixed submission:

x = int(input())
li = list(map(int, input().split()))

a = 0
Min = li[0]
for i in range(len(li)):
    if li[i] <= Min:
        Min = li[i]
        a += 1
print(a)
Buggy python submission (verdict: Time Limit Exceeded):
from functools import lru_cache
import sys
sys.setrecursionlimit(10**9)
@lru_cache(maxsize=None)
def f(n):
    if 0 < n and n  < 10:
        return n
    else:
        n = str(n)
        if int(n[-1]) == 0:
            return f(int(n)-1)
        if int(n[0]) < int(n[-1]):
            k = len(n) - 2
            n = int(n)
            if k > 0:
                return f(n-1) + int('1'*k)*2
            else:
                return f(n-1)
        elif int(n[0]) > int(n[-1]):
            k = len(n) - 1
            n = int(n)
            s = int('1'*k)*2
            return  f(n-1) + s
        else:
            k = len(n) - 2
            if k > 0:
                N = int(n)
                return f(N-1) + int('1'*k)*2  + int(n[1:-1])*2 + 3
            else:
                N = int(n)
                return f(N-1) + 3
                
p = int(input())
print(f(p))

Fixed submission:
from functools import lru_cache
import sys
sys.setrecursionlimit(10**9)
@lru_cache(maxsize=None)
def f(n):
    if 0 < n and n  < 10:
        return n
    else:
        n = str(n)
        if int(n[-1]) == 0:
            return f(int(n)-1)
        if int(n[0]) < int(n[-1]):
            k = len(n) - 2
            n = int(n)
            if k > 0:
                return f(n-1) + int('1'*k)*2
            else:
                return f(n-1)
        elif int(n[0]) > int(n[-1]):
            k = len(n) - 1
            n = int(n)
            s = int('1'*k)*2
            return  f(n-1) + s
        else:
            k = len(n) - 2
            if k > 0:
                N = int(n)
                return f(N-1) + int('1'*k)*2  + int(n[1:-1])*2 + 3
            else:
                N = int(n)
                return f(N-1) + 3
                
p = int(input())
print(f(p))
Buggy python submission (verdict: Runtime Error):
x, y = map(int, input().split())
li = []
k = 0 #カウント数
for _ in range(y):
    a, b = map(str, input().split())
    if b == 'AC':
        if a in li:
            continue
        else:
            li.append(a)
    elif b == 'WA':
        if a in li:
            continue
        else:
            k += 1
s = 0
for _ in dd:
    s += 1
            
print(s, k)

Fixed submission:
x, y = map(int, input().split())
dd = {}
c = 0 #間違い数
p = 0 #AC数
for i in range(x):
    dd[i+1] = 0
for _ in range(y):
    a, b = map(str, input().split())
    a = int(a)
    if b == 'WA':
        if dd[a] == 'o':
            continue
        else:
            dd[a] += 1
    else:
        if dd[a] == 'o':
            continue
        else:
            c += dd[a]
            p += 1
            dd[a] = 'o'
            
print(p, c)
Buggy python submission (verdict: Runtime Error):
a = int(input())
b = True
def hantei(n, x):
  for i in range(n):
    if n % i == 0:
      x = not x
      return x
while b is True:
  hantei(a, b)
  a += 1
  if not b:
    print(a)

Fixed submission:
a = int(input())
def hantei(x):
    k = 0
    for i in range(2, x//2):
        if x % i == 0:
            k += 1
    if k ==0:
        return x

c = True
while c:
    hantei(a)
    b = hantei(a)
    if b is not None:
        print(b)
        c = False
    elif b is None:
        a += 1
Buggy python submission (verdict: Runtime Error):
import math
x, y = map(int, input().split())
a = math.gcd(x, y)
print(int(x*y/a))

Fixed submission:
import fractions
x, y = map(int, input().split())
a = fractions.gcd(x, y)
b = int(x*y/a)
print(b)

Buggy python submission (verdict: Runtime Error):
import math
x, y = map(int, input().split())
a = math.gcd(x, y)
print(int(x*y/a))

Fixed submission:
import fractions
x, y = map(int, input().split())
a = fractions.gcd(x, y)
b = int(x*y/a)
print(b)

Buggy python submission (verdict: Runtime Error):
import math
x, y = map(int, input().split())
a = math.gcd(x, y)
print(int(x*y/a))

Fixed submission:
import fractions
x, y = map(int, input().split())
a = fractions.gcd(x, y)
b = int(x*y/a)
print(b)
Buggy python submission (verdict: Runtime Error):
x = int(input())
li = list(map(int, input()))
l = []
for i in range(len(li)):
    l.append(i+1-li[i])
print(min(l))

Fixed submission:
x = int(input())
li = list(map(int, input().split()))
k = 1
s = 0
for i in range(len(li)):
    if k == li[i] :
        k += 1
        s += 1
    if i == len(li)-1 and k == 1:
        s = len(li) + 1
print(len(li)-s)

Buggy python submission (verdict: Runtime Error):
x = int(input())
li = list(map(int, input()))
from collections import deque
l = deque(li)

def m(p, lis):
    for i in range(len(lis)):
        if lis.leftpop() == p:
            return i+1
    return -1

print(m(x, l))

Fixed submission:
x = int(input())
li = list(map(int, input().split()))
k = 1
s = 0
for i in range(len(li)):
    if k == li[i] :
        k += 1
        s += 1
    if i == len(li)-1 and k == 1:
        s = len(li) + 1
print(len(li)-s)
Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.buffer.readline

from collections import deque, defaultdict

#以下０オリジンで考える

n, u, v = map(int, input().split())
u, v = u-1, v-1

G = defaultdict(lambda:deque([])) #連結リスト

#以下０オリジンで考える
for _ in range(n-1):
    a, b = map(int, input().split())
    G[a-1].append(b-1)
    G[b-1].append(a-1)
    
#start位置から繋がる全ノードへの距離を求める関数、幅優先探索
#dst_dict[player][node]がplayerとnodeの距離
def bfs(start, player):
    que = deque([start, -1, 0])
    while que:
        node, par, dst = que.popleft() #par:親, dst:距離
        if len(G[node]) == 1:
            dst_dict[player][node] = dst
            
        for nxt in graph[node]:
            if nxt == par:
                continue
            que.append((nxt, node, dst+1))
            
dst_dict = [{}, {}]

bfs(u, 0)
bfs(v, 1)

max_time = 0
for k in dst_dict[0]:
    if dst_dict[0][k] < dst_dict[1][k]:
        max_time = max(max_time, dst_dict[1][k]-1)
    
print(max_time)


Fixed submission:
import sys
input = sys.stdin.buffer.readline

from collections import deque, defaultdict

#以下０オリジンで考える

n, u, v = map(int, input().split())
u, v = u-1, v-1

G = defaultdict(lambda:deque([])) #連結リスト

#以下０オリジンで考える
for _ in range(n-1):
    a, b = map(int, input().split())
    G[a-1].append(b-1)
    G[b-1].append(a-1)
    
#start位置から繋がる全ノードへの距離を求める関数、幅優先探索
#dst_dict[player][node]がplayerとnodeの距離
def bfs(start, player):
    que = deque([(start, -1, 0)])
    while que:
        node, par, dst = que.popleft() #par:親, dst:距離
        if len(G[node]) == 1:
            dst_dict[player][node] = dst
            
        for nxt in G[node]:
            if nxt == par:
                continue
            que.append((nxt, node, dst+1))
            
dst_dict = [{}, {}]

bfs(u, 0)
bfs(v, 1)

max_time = 0
for k in dst_dict[0]:
    if dst_dict[0][k] < dst_dict[1][k]:
        max_time = max(max_time, dst_dict[1][k]-1)
    
print(max_time)
Buggy python submission (verdict: Runtime Error):
def framod(n, mod, a=1):
    for i in range(1,n+1):
        a=a * i % mod
    return a

def power(n, r, mod):
    if r == 0: return 1
    if r%2 == 0:
        return power(n*n % mod, r//2, mod) % mod
    if r%2 == 1:
        return n * power(n, r-1, mod) % mod

def comb(n, k, mod):
    a=framod(n, mod)
    b=framod(k, mod)
    c=framod(n-k, mod)
    return (a * power(b, mod-2, mod) * power(c, mod-2, mod)) % mod
for i in range( 2, N + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

x, y = map(int, input().split())
if  x/y > 2 or y/x > 2:
    print(0)
else:
    if (2*x-y)%3 != 0 or (2*y - x)%3 != 0:
        print(0)
    else:
        a = (2*x-y) / 3
        b = (2*y-x) / 3
        a, b = int(a), int(b)
        mod = 10**9 + 7
        print(comb(a+b, a, mod))

Fixed submission:
def framod(n, mod, a=1):
    for i in range(1,n+1):
        a=a * i % mod
    return a

def power(n, r, mod):
    if r == 0: return 1
    if r%2 == 0:
        return power(n*n % mod, r//2, mod) % mod
    if r%2 == 1:
        return n * power(n, r-1, mod) % mod

def comb(n, k, mod):
    a=framod(n, mod)
    b=framod(k, mod)
    c=framod(n-k, mod)
    return (a * power(b, mod-2, mod) * power(c, mod-2, mod)) % mod

x, y = map(int, input().split())
if  x/y > 2 or y/x > 2:
    print(0)
else:
    if (2*x-y)%3 != 0 or (2*y - x)%3 != 0:
        print(0)
    else:
        a = (2*x-y) / 3
        b = (2*y-x) / 3
        a, b = int(a), int(b)
        mod = 10**9 + 7
        print(comb(a+b, a, mod))
Buggy python submission (verdict: Runtime Error):
n = int(input())
min_ = n -1 
for i in range(1, n**0.5+10):
  if n % i != 0:
    continue
  else:
    min_ = min(min_, i-1+n//i-1)
    
print(min_)

Fixed submission:
n = int(input())
min_ = n -1 
for i in range(1, int(n**0.5)+10):
    if n % i != 0:
        continue
    else:
        min_ = min(min_, i-1+(n//i)-1)
    
print(min_)
Buggy python submission (verdict: Runtime Error):
x, y = map(int(input().split()))
if x - 2*y >= 0:
  print(x-2*y)
else:
  print(0)


Fixed submission:
x, y = map(int, input().split())
if x - 2*y >= 0:
  print(x-2*y)
else:
  print(0)

Buggy python submission (verdict: Runtime Error):
x, y = int(input().split())
if x - 2*y >= 0:
  print(x-2*y)
else:
  print(0)

Fixed submission:
x, y = map(int, input().split())
if x - 2*y >= 0:
  print(x-2*y)
else:
  print(0)
Buggy python submission (verdict: Runtime Error):
di = {'Sunny':'Cloudy', 'Cloudy':'Rainy', 'Sunny'}
x = input()
print(di[x])



Fixed submission:
di = {'Sunny':'Cloudy', 'Cloudy':'Rainy', 'Rainy':'Sunny'}
x = input()
print(di[x])