Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
MOD = 10**9+7
N = int(input())

X = [[] for _ in range(N)]

for _ in range(N-1):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)
    
P = [-1] * N
def dfs(i):
    for j in X[i]:
        if j != 0 and P[j] < 0:
            P[j] = i
            dfs(j)

dfs(0)

for i in range(N):
    if i != 0:
        X[i].remove(P[i])

ans = 0
B = [0] * N
W = [0] * N

def dfs2(i):
    _ansb = 1
    _answ = 1
    for j in X[i]:
        __ansb, __answ = dfs2(j)
        _ansb *= __answ
        _answ *= (__ansb+__answ)
        _ansb %= MOD
        _answ %= MOD
    
    return (_ansb, _answ)

print(sum(dfs2(0)) % MOD)


Fixed submission:
import sys
sys.setrecursionlimit(1000000)

MOD = 10**9+7
N = int(input())

X = [[] for _ in range(N)]

for _ in range(N-1):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)
    
P = [-1] * N
def dfs(i):
    for j in X[i]:
        if j != 0 and P[j] < 0:
            P[j] = i
            dfs(j)

dfs(0)

for i in range(N):
    if i != 0:
        X[i].remove(P[i])

ans = 0
B = [0] * N
W = [0] * N

def dfs2(i):
    _ansb = 1
    _answ = 1
    for j in X[i]:
        __ansb, __answ = dfs2(j)
        _ansb *= __answ
        _answ *= (__ansb+__answ)
        _ansb %= MOD
        _answ %= MOD
    
    return (_ansb, _answ)

print(sum(dfs2(0)) % MOD)

Buggy python submission (verdict: Runtime Error):
N = int(input())

X = [[] for _ in range(N)]

for _ in range(N-1):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)
    
P = [-1] * N
def dfs(i):
    for j in X[i]:
        if j != 0 and P[j] < 0:
            P[j] = i
            dfs(j)

dfs(0)

for i in range(N):
    if i != 0:
        X[i].remove(P[i])

ans = 0
B = [0] * N
W = [0] * N

def dfs2(i):
    _ansb = 1
    _answ = 1
    for j in X[i]:
        __ansb, __answ = dfs2(j)
        _ansb *= __answ
        _answ *= (__ansb+__answ)
    
    return (_ansb, _answ)

print(sum(dfs2(0)))


Fixed submission:
import sys
sys.setrecursionlimit(1000000)

MOD = 10**9+7
N = int(input())

X = [[] for _ in range(N)]

for _ in range(N-1):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)
    
P = [-1] * N
def dfs(i):
    for j in X[i]:
        if j != 0 and P[j] < 0:
            P[j] = i
            dfs(j)

dfs(0)

for i in range(N):
    if i != 0:
        X[i].remove(P[i])

ans = 0
B = [0] * N
W = [0] * N

def dfs2(i):
    _ansb = 1
    _answ = 1
    for j in X[i]:
        __ansb, __answ = dfs2(j)
        _ansb *= __answ
        _answ *= (__ansb+__answ)
        _ansb %= MOD
        _answ %= MOD
    
    return (_ansb, _answ)

print(sum(dfs2(0)) % MOD)
Buggy python submission (verdict: Time Limit Exceeded):
def mmult(A, B):
    global mod
    n, m, l = len(A), len(B), len(B[0])
    ret = [[0]*l for _ in range(n)]
    for i in range(n):
        for j in range(m):
            for k in range(l):
                ret[i][k] = (ret[i][k]+A[i][j]*B[j][k])%mod
    return ret
def mpow(A, n):
    if n == 0: return [[1 if i==j else 0 for j in range(len(A))] for i in range(len(A))]
    if n % 2: return mmult(mpow(A, n-1), A)
    return mpow(mmult(A, A), n//2)

mod = 10**9+7
N, K = map(int, input().split())
X = [[int(a) for a in input().split()] for _ in range(N)]
print(sum([sum(x) for x in mpow(X, K)]) % mod)

Fixed submission:
def mmult(A, B):
    global mod
    n, m, l = len(A), len(B), len(B[0])
    ret = [[0]*l for _ in range(n)]
    for i in range(n):
        for j in range(m):
            for k in range(l):
                ret[i][k] = (ret[i][k]+A[i][j]*B[j][k])%mod
    return ret
def mpow(A, n):
    if n == 0: return [[1 if i==j else 0 for j in range(len(A))] for i in range(len(A))]
    if n % 2: return mmult(mpow(A, n-1), A)
    return mpow(mmult(A, A), n//2)

mod = 10**9+7
N, K = map(int, input().split())
X = [[int(a) for a in input().split()] for _ in range(N)]
print(sum([sum(x) for x in mpow(X, K)]) % mod)
Buggy python submission (verdict: Time Limit Exceeded):
K = input()
N = len(K)
D = int(input())
Y = [0] * D
P = 10**9+7
a = 0
for i in range(N):
    nY = [0] * D
    c = int(K[i])
    for j in range(10):
        if j < c:
            nk = (j+a)%D
            nY[nk] += 1

        for k in range(D):
            nk = (j+k)%D
            nY[nk] += Y[k]
        
    a = (a+c) % D
    Y = nY
print((Y[0] - 1 + (a==0)) % P)


Fixed submission:
K = input()
N = len(K)
D = int(input())
Y = [0] * D
P = 10**9+7
a = 0
for i in range(N):
    nY = [0] * D
    c = int(K[i])
    for j in range(10):
        if j < c:
            nk = (j+a) % D
            nY[nk] = (nY[nk] + 1) % P

        for k in range(D):
            nk = (j+k) % D
            nY[nk] = (nY[nk] + Y[k]) % P
        
    a = (a+c) % D
    Y = nY
print((Y[0] - 1 + (a==0)) % P)

Buggy python submission (verdict: Time Limit Exceeded):
K = input()
N = len(K)
D = int(input())
X = [0] * D
Y = [0] * D
X[0] = 1
P = 10**9+7
for i in range(N):
    nX = [0] * D
    nY = [0] * D
    for j in range(10):
        for k in range(D):
            nk = (j+k)%D
            nY[nk] += Y[k]
            if j < int(K[i]):
                nY[nk] = (nY[nk] + X[k]) % P
            elif j == int(K[i]):
                nX[nk] = (nX[nk] + X[k]) % P
    
    X, Y = nX, nY
print((X[0] + Y[0] - 1) % P)


Fixed submission:
K = input()
N = len(K)
D = int(input())
Y = [0] * D
P = 10**9+7
a = 0
for i in range(N):
    nY = [0] * D
    c = int(K[i])
    for j in range(10):
        if j < c:
            nk = (j+a) % D
            nY[nk] = (nY[nk] + 1) % P

        for k in range(D):
            nk = (j+k) % D
            nY[nk] = (nY[nk] + Y[k]) % P
        
    a = (a+c) % D
    Y = nY
print((Y[0] - 1 + (a==0)) % P)
Buggy python submission (verdict: Runtime Error):
K = int(input())

if K <= 500:
    print(K)
    for i in range(K):
        print(*([i+1]*K))
elif K % 4 == 0:
    print(K // 2)
    for i in range(K // 2):
        print(*([i+1, i+1+K//2] * (K//4)))
else:
    print(1//0)
    


Fixed submission:
K = int(input())
M = 1000

def a(i, j):
    tmp = (i - j) % (M//2) + 1
    if j % 2 == 0 or M + 1 - tmp > K:
        return tmp
    else:
        return M + 1 - tmp
    
if K <= M//2:
    print(K)
    for i in range(K):
        print(*([i+1]*K))
else:
    print(M//2)
    for j in range(M//2):
        print(*([a(i, j) for i in range(M//2)]))
Buggy python submission (verdict: Runtime Error):
N = int(input())

X = [[] for i in range(N)]
P = [-1] * N

for i in range(N-1):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)


def set_parent(i):
    # print(i)
    for a in X[i]:
        if a != P[i]:
            P[a] = i
            # print(a)
            X[a].remove(i)
            set_parent(a)
    
set_parent(0)

B = [-1] * N
def set_block(i):
    for a in X[i]:
        B[a] = max(i, B[i])
        set_block(a)

B_id = [-1] * N
B_id_cnt = [0] * N
def BID(i):
    for a in X[i]:
        if a > B[i]:
            B_id[a] = a
        else:
            B_id[a] = B_id[i]
            
        # print(a, B_id)
        B_id_cnt[B_id[a]] += 1
        BID(a)
        
Ans = [1] * N
def flow(i):
    for a in X[i]:
        if B_id[a] == B_id[i]:
            Ans[a] = Ans[i]
        else:
            Ans[a] = Ans[i] + B_id_cnt[a]
        flow(a)

set_block(0)


# print("X=", X) # 子リスト
# print("P=", P) # 親
# print("B=", B) # Block
# print(B_id) # BlockのID
# print(B_id_cnt) # BlockのID
# print(Ans)
print(" ".join(map(str, Ans[1:])))


Fixed submission:
s = input()
n = len(s)
a = 0
b = 0
for i in range(n):
    if s[i] == "W":
        a += 1
        b += i
        
print(b - a*(a-1)//2)
Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * (10 ** 8 * (2**A))

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")

Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * (10 ** 8 * (A*2+1))

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")

Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * (10 ** 8 * (A*2+2))

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")

Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * (10 ** 8 * (A*2+2))

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")

Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * (10 ** 8 * (A*2+2))

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")

Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * (10 ** 8 * (A*2+2))

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")

Buggy python submission (verdict: Runtime Error):
A = 25 - int(input()) # 0,1,2,3
X = [0] * 10 ** (A+8)

Fixed submission:
D = int(input())
if D == 25:
    print("Christmas")
elif D == 24:
    print("Christmas Eve")
elif D == 23:
    print("Christmas Eve Eve")
else:
    print("Christmas Eve Eve Eve")
Buggy python submission (verdict: Runtime Error):
N, K = map(int, input().split())
A = [0] + [int(a) for a in input().split()]
for i in range(N):
    A[i+1] += A[i]
S = []
for i in range(1, N+1):
    for j in range(i):
        S.append(A[i] - A[j])
l, r = 0, 1 << 50
while r - l > 1:
    m = (l+r) // 2
    if len([1 for i in range(len(S)) if S[i] & m == m]) >= K:
        l = m
    else:
        r = m
print(l)

Fixed submission:
N, K = map(int, input().split())
A = [0] + [int(a) for a in input().split()]
for i in range(N):
    A[i+1] += A[i]
S = []
for i in range(1, N+1):
    for j in range(i):
        S.append(A[i] - A[j])
l, r = 0, 1 << 50
while r - l > 1:
    m = (l+r) // 2
    if len([1 for i in range(len(S)) if S[i] & m == m]) >= K:
        l = m
    else:
        r = m
print(l)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())
A = [0] + [int(a) for a in input().split()]
for i in range(N):
    A[i+1] += A[i]
S = []
for i in range(1, N+1):
    for j in range(i):
        S.append(A[i] - A[j])
l, r = 0, 1 << 50
while r - l > 1:
    m = (l+r) // 2
    if len([1 for i in range(len(S)) if S[i] & m == m]) >= K:
        l = m
    else:
        r = m
print(l)

Fixed submission:
N, K = map(int, input().split())
A = [0] + [int(a) for a in input().split()]
for i in range(N):
    A[i+1] += A[i]
S = []
for i in range(1, N+1):
    for j in range(i):
        S.append(A[i] - A[j])
l, r = 0, 1 << 50
while r - l > 1:
    m = (l+r) // 2
    if len([1 for i in range(len(S)) if S[i] & m == m]) >= K:
        l = m
    else:
        r = m
print(l)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [int(a) for a in input().split()]
def fact(n):
    if n==0:
        return 1
    else:
        return n*fact(n-1) % p
    
def mod_combination(n, k, mod):
    # nCk (mod m)
    def mod_permutation(n, k, mod):
        if n<=k:
            return 1
        else:
            return (n * mod_permutation(n-1,k,mod))%mod

    def mod_inv_permutation(k, mod):
        k, mod = int(k), int(mod)
        if k<=1:
            return 1
        else:
            return (pow(k,mod-2,mod) * mod_inv_permutation(k-1, mod))%mod

    return (mod_permutation(n,n-k,mod) * mod_inv_permutation(k, mod))%mod

X = [[0,0],[0,1,0]]
p = 10**9 + 7
for i in range(2, N+1):
#    print ("i=",i)
    s = [0] * (i+2)
    for j in range(i):
        a = j + 1 - 1
        b = i - (j + 1)
#        print (i, j, a, b)
#        print ("Bef", s)
        for k in range(a):
#            print ("s[", k+1, "] +=", X[a][k+1]*mod_combination(a+b,a,p)*fact(b)+fact(i-1))
            s[k+1] += ((X[a][k+1]*mod_combination(a+b,a,p) % p)*fact(b) % p +fact(i-1)) % p
        for k in range(b):
#            print ("s[", i-k, "] +=", X[b][k+1]*mod_combination(a+b,a,p)*fact(a)+fact(i-1))
            s[i-k] += ((X[b][k+1]*mod_combination(a+b,a,p) % p) *fact(a) % p +fact(i-1)) % p
#        print ("s[", j+1, "] +=", fact(i-1))
        s[j+1] += fact(i-1)
#        print ("Aft", s)
    X.append(s)
#    print (X)

ans = 0
for i in range(N):
    ans += X[N][i+1] * A[i]
    ans %= p
print (ans)

Fixed submission:
def mod_inv(n,p):
    if n<0:
        return - mod_inv(-n,p) % p
    if n>p:
        return mod_inv(n % p, p)
    
    def mod_inv_calc(a,b):
        if b==0:
            return (a,1)
        else:
            s,t = mod_inv_calc(b, a % b)
            d = a//b
            return (t, -t*d+s)

    return mod_inv_calc(p,n)[1] % p

N = int(input())
A = [int(a) for a in input().split()]
p = 10**9+7
inv_list = [mod_inv(i+1,p) for i in range(N+2)]

fact_list = [1]
for i in range(N):
    fact_list.append(fact_list[i] * (i+1) % p)
s = 0
sum_list = [inv_list[i] * fact_list[N] % p for i in range(N+2)]

for i in range(N):
    s += inv_list[i]
    
s *= fact_list[N]
s %= p
ans = 0
for i in range(N):
    ans += A[i]*s
    ans %= p
    s += (sum_list[i+1] - sum_list[N-i-1])
    s %= p
    
print (ans)
Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
a = M//N
def gcd(a, b):
    if b == 0:
        return a
    else:
        return gcd(b, a % b)

ma = 0
for i in range(a, 0, -1):
    if M % i == 0:
        ma = max(ma, i)
    
print(ma)


Fixed submission:
N, M = map(int, input().split(" "))
flg = 0
for i in range(N, M+1):
    if M % i == 0:
        print (M//i)
        flg = 1
        break
    if i**2 > M:
        break

if flg == 0:
    for i in range(M//N, 0, -1):
        if M % i == 0:
            print (i)
            break

Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
a = M//N
def gcd(a, b):
    if b == 0:
        return a
    else:
        return gcd(b, a % b)

ma = gcd(a, M)
for i in range(a, 0, -1):
    ma = max(ma, gcd(i, M))
    
print(ma)


Fixed submission:
N, M = map(int, input().split(" "))
flg = 0
for i in range(N, M+1):
    if M % i == 0:
        print (M//i)
        flg = 1
        break
    if i**2 > M:
        break

if flg == 0:
    for i in range(M//N, 0, -1):
        if M % i == 0:
            print (i)
            break
Buggy python submission (verdict: Time Limit Exceeded):
x = [c  for c in input()]

n = len(x)
ret=[]
for i in range(n-1):
    ret.append([0,0])

if x[n-1] == "1":
    print (-1)
elif x[0] == "0":
    print (-1)
else:
    flg = 1
    for i in range(int((n-1)/2)):
        if x[i] != x[n-1-i-1]:
            flg = 0
    if flg == 0:
        print (-1)
    else:
        for i in range(int((n-1)/2)):
            if x[i] == "1":
                ret[i] = [i+1,i+2]
                ret[n-i-2] = [n-i-1+1,n-i-2+1]
            else:
                for j in range(i):
                    if ret[j][1] == i+1:
                        ret[j][1] = i+2
                    if ret[n-j-2][1] == n-i-1+1:
                        ret[n-j-2][1] = n-i-2+1
                ret[i] = [i+1,i+2]
                ret[n-i-2] = [n-i-1+1,n-i-2+1]
                
        if n % 2 == 0:
            i = int(n/2)-1
            if x[i] == "1":
                ret[i] = [i+1,i+2]
            else:
                for j in range(i):
                    if ret[n-j-2][1] == n-i-1+1:
                        ret[n-j-2][1] = n-i-2+1
                ret[i] = [i+1,i+2]
                
        
        for i in range(n-1):
            print ("{0} {1}".format(ret[i][0], ret[i][1]))

Fixed submission:
x = [c  for c in input()]

n = len(x)
ret=[]
for i in range(n-1):
    ret.append([0,0])

if x[n-1] == "1":
    print (-1)
elif x[0] == "0":
    print (-1)
else:
    flg = 1
    for i in range(int((n-1)/2)):
        if x[i] != x[n-1-i-1]:
            flg = 0
    if flg == 0:
        print (-1)
    else:
        a=1
        b=n
        for i in range(int((n-2)/2)):
            if x[i] == "1":
                ret[i] = [a,i+2]
                ret[n-i-2] = [b,n-i-2+1]
                a=i+2
                b=n-i-2+1
            else:
                ret[i] = [a,i+2]
                ret[n-i-2] = [b,n-i-2+1]
                
        if n % 2 == 1:
            i = int((n-3)/2)
            if x[i] == "1":
                ret[i] = [a,i+2]
                ret[n-i-2] = [b,n-i-2+1]
            else:
                tmp = b
                for j in range(i):
                    if ret[n-j-2][1] == b:
                        ret[n-j-2][1] = a
                    if ret[n-j-2][0] == b:
                        ret[n-j-2][0] = a
                ret[i] = [a,i+2]
                ret[n-i-2] = [a,tmp]
        else:
            i = int(n/2)-1
            if x[i] == "1":
                ret[i] = [a,b]
            else:
                tmp = b
                for j in range(i):
                    if ret[n-j-2][1] == b:
                        ret[n-j-2][1] = a
                    if ret[n-j-2][0] == b:
                        ret[n-j-2][0] = a
                ret[i] = [a,b]
                
        
        for i in range(n-1):
            print ("{0} {1}".format(ret[i][0], ret[i][1]))
Buggy python submission (verdict: Runtime Error):
N = int(input())
D = [int(input()) for i in range(N)]
D = sorted(D)[::-1]

DtoI = {}
pD = [-1] * N
L = [1] * N
T = [0] * N

Y = {}
cnt = 0
for i in range(N):
    DtoI[D[i]] = i

for i in range(N):
    if D[i] in Y:
        for y in Y[D[i]]:
            L[i] += L[y]
            T[i] += T[y] + L[y]
            cnt += 1
        
    p = N - 2 * L[i]
    if p <= 0 or i == N-1:
        pd = -1
    else:
        pd = D[i] - p
    pD[i] = pd
    
    if pd not in Y:
        Y[pd] = []
    Y[pd].append(i)

if pD[-2] < 0:
    print(-1)
else:
    for i in range(N-1):
        print (i + 1, DtoI[pD[i]] + 1)


Fixed submission:
def main():
    N = int(input())
    D = [int(input()) for i in range(N)]
    C = [1] * N
    T = [0] * N
    DI = {}
    for i in range(len(D)):
        DI[D[i]] = i
    D = sorted(D)
    P = [-1] * N
    while len(D) > 1:
        d = D.pop()
        i = DI[d]
        nd = d - N + C[i] * 2
        if nd in DI:
            ni = DI[nd]
        else:
            print(-1)
            return
        P[i] = ni
        C[ni] += C[i]
        T[ni] += T[i] + C[i]
    
    if D[0] == T[DI[D[0]]]:
        for i in range(N):
            if P[i] >= 0: print(i+1, P[i]+1)
    else:
        print(-1)

main()

Buggy python submission (verdict: Runtime Error):
N = int(input())
D = [int(input()) for i in range(N)]
D = sorted(D)[::-1]

for i in range(N):
    D[i] -= 0

DtoI = {}
pD = [-1] * N
L = [1] * N
T = [0] * N

Y = {}
cnt = 0
for i in range(N):
    DtoI[D[i]] = i

for i in range(N):
    if D[i] in Y:
        for y in Y[D[i]]:
            L[i] += L[y]
            T[i] += T[y] + L[y]
            cnt += 1
        
    p = N - 2 * L[i]
    if p <= 0 or i == N-1:
        pd = -1
    else:
        pd = D[i] - p
    pD[i] = pd
    
    if pd not in Y:
        Y[pd] = []
    Y[pd].append(i)

for i in range(N-1):
    print (i + 1, DtoI[pD[i]] + 1)

Fixed submission:
def main():
    N = int(input())
    D = [int(input()) for i in range(N)]
    C = [1] * N
    T = [0] * N
    DI = {}
    for i in range(len(D)):
        DI[D[i]] = i
    D = sorted(D)
    P = [-1] * N
    while len(D) > 1:
        d = D.pop()
        i = DI[d]
        nd = d - N + C[i] * 2
        if nd in DI:
            ni = DI[nd]
        else:
            print(-1)
            return
        P[i] = ni
        C[ni] += C[i]
        T[ni] += T[i] + C[i]
    
    if D[0] == T[DI[D[0]]]:
        for i in range(N):
            if P[i] >= 0: print(i+1, P[i]+1)
    else:
        print(-1)

main()
Buggy python submission (verdict: Runtime Error):
from functools import reduce

def gcd(a, b):

    if b == 0:
        return a
    else:
        return gcd(b, a % b)

def gcd_list(numbers):
    return reduce(gcd, numbers)

N, X = map(int, input().split(" "))
Xi = [int(a) for a in input().split()]

def minusX(a):
    return abs(a-X)

Xi = map(minusX, Xi)

d = gcd_list(Xi)
print (d)

Fixed submission:
a, b = map(int, input().split(" "))
if a % 2 == 1 and b % 2 == 1:
    print ("Yes")
else:
    print ("No")

Buggy python submission (verdict: Runtime Error):
Print("Yes")

Fixed submission:
a, b = map(int, input().split(" "))
if a % 2 == 1 and b % 2 == 1:
    print ("Yes")
else:
    print ("No")
Buggy python submission (verdict: Runtime Error):
N = int(input())
W = [input() for i in range(N)]

if [W[i][-1] for i in range(N-1)] == [W[i+1][0] for i in range(N-1)] and len(list(set(W))) = len(W):
    print ("Yes")
else:
    print ("No")

Fixed submission:
N = int(input())
Ws = [input() for i in range(N)]

ret = "Yes"
if len(Ws) != len(list(set(Ws))):
    ret = "No"
    
for i in range(N-1):
    if Ws[i][-1] != Ws[i+1][0]:
        ret = "No"
    
    
print (ret)
Buggy python submission (verdict: Runtime Error):
K, N = map(int, input().split())
P = 998244353
fa = [1]
for i in range(1, 10000):
    fa.append(fa[-1] * i % P)
fainv = [pow(fa[-1], P-2, P)]
for i in range(1, 10000)[::-1]:
    fainv.append(fainv[-1] * i % P)
fainv = fainv[::-1]

def C(a, b):
    if not (a >= 0 and 0 <= b <= a): return 0
    return fa[a] * fainv[a-b] * fainv[b] % P

A = []
for i in range(1, K-2):
    s = 0
    for j in range(i+1):
        s += C(N+K-1-2*j, K-1) * C(i, j) * (-1) ** j
        s %= P
    A.append(s)
for a in A:
    print(a)
    print(a)
print(A[-1])
for a in A[::-1][1:]:
    print(a)
    print(a)

Fixed submission:
K, N = map(int, input().split())
P = 998244353
fa = [1]
for i in range(1, 10000):
    fa.append(fa[-1] * i % P)
fainv = [pow(fa[-1], P-2, P)]
for i in range(1, 10000)[::-1]:
    fainv.append(fainv[-1] * i % P)
fainv = fainv[::-1]
def C(a, b):
    if not (a >= 0 and 0 <= b <= a): return 0
    return fa[a] * fainv[a-b] * fainv[b] % P

A = []
for i in range(1, (K+1)//2+1):
    s = 0
    for j in range(i+1):
        s += C(N+K-1-2*j, K-1) * C(i, j) * (-1) ** j
        s %= P
    A.append(s)
for i in range(2*K-1):
    print(A[min(i//2, (2*K-i-2)//2)])
Buggy python submission (verdict: Runtime Error):
S = input()
K = int(input())


a=0
b=0
for i in range(len(S)):
    if int(S[i]) > 1:
        a=i
        b=S[i]
        break
# print(a)
# print(b)
if K< a:
    print (S[a])
    
else:
    print (b)
    
else:
    print (b)

Fixed submission:
S = input()
K = int(input())

for i in range(K):
    if S[i] != "1":
        print(S[i])
        break
else:
    print("1")
Buggy python submission (verdict: Runtime Error):
N, M = map(int, input().split(" "))
A = [int(a) for a in input().split()]
 
tmp=0
B=[0]
for i in A:
    tmp += A[i]
    tmp = tmp % M
    B.append(tmp)
 
B.sort()
cnt=0
ret=0
for i in range(len(B)):
    if i ==0:
        cnt += 1
        prev=B[0]
        
    else:
        if B[i] == prev:
            cnt += 1
            
        else:
            ret += int(cnt*(cnt-1)/2)
            prev = B[i]
            cnt = 1
 
ret += int(cnt*(cnt-1)/2)
 
print (ret)

Fixed submission:
N, K = map(int, input().split(" "))
if N % K ==0:
    print (0)
else:
    print(1)

Buggy python submission (verdict: Runtime Error):
N, M = map(int, input().split(" "))
A = [int(a) for a in input().split()]

tmp=0
B=[0]
for i in A:
    tmp += A[i]
    tmp = tmp % M
    B.append(tmp)

B.sort()
print (B)
cnt=0
ret=0
for i in range(len(B)):
    if i ==0:
        cnt += 1
        prev=B[0]
        
    else:
        if B[i] == prev:
            cnt += 1
            
        else:
            ret += int(cnt*(cnt-1)/2)
            prev = B[i]
            cnt = 1

ret += int(cnt*(cnt-1)/2)

print (ret)

Fixed submission:
N, K = map(int, input().split(" "))
if N % K ==0:
    print (0)
else:
    print(1)