Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
import fractions
def lcm(a,b):
    return a*b//fractions.gcd(a,b)

a,b,c,d=map(int,input().split())

P=[c,d,lcm(c,d)]
A=[]
for p in P:
    if a%p==0:
        left=a//p
    else:
        left=a//p+1
    right=b//p
    if left<=right:
        A.append(right-left+1)
print(b-a+1-A[0]-A[1]+A[2])

Fixed submission:
import fractions
def lcm(a,b):
    return a*b//fractions.gcd(a,b)

a,b,c,d=map(int,input().split())

P=[c,d,lcm(c,d)]
A=[]
for p in P:
    if a%p==0:
        left=a//p
    else:
        left=a//p+1
    right=b//p
    if left<=right:
        A.append(right-left+1)
    else:
        A.append(0)
print(b-a+1-A[0]-A[1]+A[2])
Buggy python submission (verdict: Runtime Error):
import heapq as hq

N,K=map(int,input().split())
V=list(map(int,input().split()))

ans=0
for i in range(1,min(N,K)+1): #取り出す個数
    for j in range(i+1):
        A=[]
        hq.heapify(A) #左から取り出す個数
        for k in range(j):
            hq.heappush(A,V[k])
        for k in range(i-j):
            hq.heappush(A,V[n-k-1])
        p=min(i,K-i) #しまえる個数
        while p>0:
            if A[0]<0:
                hq.heappop(A)
                p-=1
            else:
                break
        ans=max(sum(A),ans)
print(ans)

Fixed submission:
import heapq as hq

N,K=map(int,input().split())
V=list(map(int,input().split()))

ans=0
for i in range(1,min(N,K)+1): #取り出す個数
    for j in range(i+1):
        A=[]
        hq.heapify(A) #左から取り出す個数
        for k in range(j):
            hq.heappush(A,V[k])
        for k in range(i-j):
            hq.heappush(A,V[N-k-1])
        p=min(i,K-i) #しまえる個数
        while p>0:
            if A[0]<0:
                hq.heappop(A)
                p-=1
            else:
                break
        ans=max(sum(A),ans)
print(ans)
Buggy python submission (verdict: Runtime Error):
n,m=map(int,input().split())
l=0
r=n+1
for i in range(m):
    a,b=map(int,input().split())
    l=max(l,a)
    r=min(r,b)
    if l>r:
        print(0)
        sys.exit()
print(r-l+1)

Fixed submission:
import sys

n,m=map(int,input().split())
l=0
r=n+1
for i in range(m):
    a,b=map(int,input().split())
    l=max(l,a)
    r=min(r,b)
    if l>r:
        print(0)
        sys.exit()
print(r-l+1)
Buggy python submission (verdict: Runtime Error):
import sys
input=sys.stdin.readline

n=int(input())
G=[[] for i in range(n)]
for i in range(n-1):
    u,v,w=map(int,input().split())
    u-=1
    v-=1
    G[u].append([v,w])
    G[v].append([u,w])

A=[0]*n
def dfs(s,p=-1):
    for g in G[s]:
        if g[0]!=p:
            A[g[0]]=A[s]+g[1]
            dfs(g[0],s)

dfs(0)
for a in A:
    if a%2==0:
        print(0)
    else:
        print(1)

Fixed submission:
import sys
input=sys.stdin.readline
sys.setrecursionlimit(10**8)

n=int(input())
G=[[] for i in range(n)]
for i in range(n-1):
    u,v,w=map(int,input().split())
    u-=1
    v-=1
    G[u].append([v,w])
    G[v].append([u,w])

A=[0]*n
def dfs(s,p=-1):
    for g in G[s]:
        if g[0]!=p:
            A[g[0]]=A[s]+g[1]
            dfs(g[0],s)

dfs(0)
for a in A:
    if a%2==0:
        print(0)
    else:
        print(1)
Buggy python submission (verdict: Runtime Error):
n,k=map(int,input().split())
S=input()

now=S[0]
cnt=1
A=[] #個数配列
for i in range(n-1):
    if S[i+1]==now:
        cnt+=1
    else:
        A.append(cnt)
        cnt=1
        now=S[i+1]
if cnt>0:
    A.append(cnt)
l=len(A)
    
if S[0]=="0":
    if l<=2*k:
        ans=n
    elif 2*k+1<=l<=2*k+2:
        ans=max(sum(A[:2*k]),sum(A[1:]))
    else:
        ans=max(sum(A[:2*k]),sum(A[1:2*k+2]))
        cnt=ans
        for i in range((l-2*k-2)//2):
            cnt-=A[2*i+2]+A[2*i+3]
            cnt+=A[2*k+2*i+2]+A[2*k+2*i+3]
            ans=max(cnt,ans)
        if l%2!=0:
            ans=max(A[l-2*k:],ans)
else:
    if l<=2*k+1:
        ans=n
    else:
        ans=sum(A[:2*k+1])
        cnt=ans
        for i in range((l-2*k-1)//2):
            cnt-=A[2*i]+A[2*i+1]
            cnt+=A[2*k+2*i+1]+A[2*k+2*i+2]
            ans=max(cnt,ans)
        if l%2!=1:
            ans=max(A[l-2*k-1:],ans)
print(ans)

Fixed submission:
n,k=map(int,input().split())
S=input()

now=S[0]
cnt=1
A=[] #個数配列
for i in range(n-1):
    if S[i+1]==now:
        cnt+=1
    else:
        A.append(cnt)
        cnt=1
        now=S[i+1]
if cnt>0:
    A.append(cnt)
l=len(A)
    
if S[0]=="0":
    if l<=2*k:
        ans=n
    elif 2*k+1<=l<=2*k+2:
        ans=max(sum(A[:2*k]),sum(A[1:]))
    else:
        ans=max(sum(A[:2*k]),sum(A[1:2*k+2]))
        cnt=sum(A[1:2*k+2])
        for i in range((l-2*k-2)//2):
            cnt-=A[2*i+1]+A[2*i+2]
            cnt+=A[2*k+2*i+2]+A[2*k+2*i+3]
            ans=max(cnt,ans)
        if l%2!=0:
            ans=max(sum(A[l-2*k:]),ans)
else:
    if l<=2*k+1:
        ans=n
    else:
        ans=sum(A[:2*k+1])
        cnt=ans
        for i in range((l-2*k-1)//2):
            cnt-=A[2*i]+A[2*i+1]
            cnt+=A[2*k+2*i+1]+A[2*k+2*i+2]
            ans=max(cnt,ans)
        if l%2==0:
            ans=max(sum(A[l-2*k:]),ans)
print(ans)
Buggy python submission (verdict: Runtime Error):
import heapq as hq

n,k=map(int,input().split())
A=[]
S0=[] #種類が増えない寿司
S1=[] #種類が増える寿司
for i in range(n):
    t,d=map(int,input().split())
    A.append([t,d])
A=list(reversed(sorted(A)))

now=0
for i in range(n):
    t=A[i][0]
    d=A[i][1]
    if now==t:
        S0.append(-d)
    else:
        S1.append(-d)
        now=t
hq.heapify(S0)
hq.heapify(S1)
C=[] #消し得る寿司のストック(S0から出したもの)

x=0 #おいしさの合計
y=0 #種類数
for i in range(k):
    if S1[0]<=S0[0]:
        x+=-hq.heappop(S1)
        y+=1
    else:
        s0=-hq.heappop(S0)
        x+=s0
        hq.heappush(C,s0)
ans=x+y**2

for i in range(min(len(S1),len(C))):
    c=hq.heappop(C)
    s1=-hq.heappop(S1)
    x+=s1-c
    y+=1
    ans=max(x+y**2,ans)
print(ans)

Fixed submission:
import heapq as hq

n,k=map(int,input().split())
A=[]
S0=[] #種類が増えない寿司
S1=[] #種類が増える寿司
for i in range(n):
    t,d=map(int,input().split())
    A.append([t,d])
A=list(reversed(sorted(A)))

now=0
for i in range(n):
    t=A[i][0]
    d=A[i][1]
    if now==t:
        S0.append(-d)
    else:
        S1.append(-d)
        now=t
hq.heapify(S0)
hq.heapify(S1)
C=[] #消し得る寿司のストック(S0から出したもの)

x=0 #おいしさの合計
y=0 #種類数
for i in range(k):
    if len(S0)==0:
        x+=-hq.heappop(S1)
        y+=1
        continue
    if len(S1)==0:
        s0=-hq.heappop(S0)
        x+=s0
        hq.heappush(C,s0)
        continue
    if S1[0]<=S0[0]:
        x+=-hq.heappop(S1)
        y+=1
    else:
        s0=-hq.heappop(S0)
        x+=s0
        hq.heappush(C,s0)
ans=x+y**2

for i in range(min(len(S1),len(C))):
    c=hq.heappop(C)
    s1=-hq.heappop(S1)
    x+=s1-c
    y+=1
    ans=max(x+y**2,ans)
print(ans)
Buggy python submission (verdict: Runtime Error):
import math
def findFactors(n):
    now=n
    f=[]
    while now%2==0:
        now//=2
        f.append(2)
    p=3
    while p<=math.sqrt(n):
        while now%p==0:
            now//=p
            f.append(p)
        p+=2
        if now==1:
            break
    if now>math.sqrt(n):
        f.append(now)
    return f

def cmb(n,r):
    if (r<0 or r>n):
        return 0
    r=min(r,n-r)
    return g1[n]*g2[r]*g2[n-r]%mod

mod=10**9+7
N=10**5+100
g1=[1,1]
g2=[1,1]
inverse=[0,1]

#n!とその逆元を求めておく
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)

n,m=map(int,input().split())
F=findFactors(m)
ans=1

now=F[0]
cnt=0
for f in F:
    if f==now:
        cnt+=1
    else:
        ans*=cmb(n-1+cnt,cnt)
        ans%=mod
        now=f
        cnt=1
ans*=cmb(n-1+cnt,cnt)
ans%=mod
print(ans)

Fixed submission:
import math
import sys

def findFactors(n):
    now=n
    f=[]
    while now%2==0:
        now//=2
        f.append(2)
    p=3
    while p<=math.sqrt(n):
        while now%p==0:
            now//=p
            f.append(p)
        p+=2
        if now==1:
            break
    if now>math.sqrt(n):
        f.append(now)
    return f

def cmb(n,r):
    if (r<0 or r>n):
        return 0
    r=min(r,n-r)
    return g1[n]*g2[r]*g2[n-r]%mod

mod=10**9+7
N=10**5+100
g1=[1,1]
g2=[1,1]
inverse=[0,1]

#n!とその逆元を求めておく
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)

n,m=map(int,input().split())
if m==1:
    print(1)
    sys.exit()

F=findFactors(m)
ans=1

now=F[0]
cnt=0
for f in F:
    if f==now:
        cnt+=1
    else:
        ans*=cmb(n-1+cnt,cnt)
        ans%=mod
        now=f
        cnt=1
ans*=cmb(n-1+cnt,cnt)
ans%=mod
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
S=input()
A=0 #Aの数
B=0 #ABの数
C=0 #ABCの数
n=1 #通り数
mod=10**9+7
for s in S:
    if s=="?":
        C=3*C+B
        B=3*B+A
        A=3*A+n
        n*=3
    elif s=="A":
        A+=n
    elif s=="B":
        B+=A
    else:
        C+=B
    A%=mod
    B%=mod
    C%=mod
print(C)

Fixed submission:
S=input()
A=0 #Aの数
B=0 #ABの数
C=0 #ABCの数
n=1 #通り数
mod=10**9+7
for s in S:
    if s=="?":
        C=3*C+B
        B=3*B+A
        A=3*A+n
        n*=3
    elif s=="A":
        A+=n
    elif s=="B":
        B+=A
    else:
        C+=B
    A%=mod
    B%=mod
    C%=mod
    n%=mod
print(C)
Buggy python submission (verdict: Runtime Error):
s=input()
if(s="ABC"):
    print("ARC")
else:
    print("ABC")

Fixed submission:
s=input()
if(s=="ABC"):
    print("ARC")
else:
    print("ABC")

Buggy python submission (verdict: Runtime Error):
s=inpput()
if(s="ABC"):
    print("ARC")
else:
    print("ABC")

Fixed submission:
s=input()
if(s=="ABC"):
    print("ARC")
else:
    print("ABC")
Buggy python submission (verdict: Runtime Error):
n=input()

print(n*n*n)

Fixed submission:
n=int(input())
print(n**3)
Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
a=[]

for i in range(n):
    a.append(int(input()))

Max=max(a)
for i in range(n):
    b=a[:]
    if(b[i]==Max):
        del b[i]
        print(max(b))
    else:
        print(Max)

Fixed submission:
n = int(input())
a = []

for i in range(n):
    a.append(int(input()))

Max = max(a)
if(a.count(Max)>1):
    for _ in range(n):
        print(Max)
else:
    for i in range(n):
        if(a[i]==Max):
            a[i]=0
            print(max(a))
        else:
            print(Max)

Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
a=[]

for i in range(n):
    a.append(int(input()))

for i in range(n):
    b=a[:]
    del b[i]
    print(max(b))

Fixed submission:
n = int(input())
a = []

for i in range(n):
    a.append(int(input()))

Max = max(a)
if(a.count(Max)>1):
    for _ in range(n):
        print(Max)
else:
    for i in range(n):
        if(a[i]==Max):
            a[i]=0
            print(max(a))
        else:
            print(Max)
Buggy python submission (verdict: Runtime Error):
n,x=map(int,input().split())
l=list(map(int,input().split()))

ans=0
d=0

for i in range(n):
    d+=l[i]
    ans+=1
    if(d>x):
        break

if(i=n-1):
    ans-=1
print(ans)


Fixed submission:
n,x=map(int,input().split())
l=list(map(int,input().split()))

ans=0
d=0

for i in range(n):
    d+=l[i]
    if(d<=x):
        ans+=1
        
print(ans+1)

Buggy python submission (verdict: Runtime Error):
n,x=map(int,input().split())

l=list(map(int,input().split()))

ans=0
d=0

for i in range(n+1):
    d+=l[i]
    ans+=1
    if(d>x):
        break
        
print(ans)

Fixed submission:
n,x=map(int,input().split())
l=list(map(int,input().split()))

ans=0
d=0

for i in range(n):
    d+=l[i]
    if(d<=x):
        ans+=1
        
print(ans+1)
Buggy python submission (verdict: Runtime Error):
import math
n=int(input())
a=[int(x) for x in input().split()]
x=1
for i in range(n):
    x=int(a[i]*x/math.gcd(a[i],x))

x-=1
ans=0

for i in range(n):
    ans+=x%a[i]

print(ans)

Fixed submission:
n=int(input())
a=[int(x) for x in input().split()]
print(sum(a)-n)
Buggy python submission (verdict: Time Limit Exceeded):
k,s=map(int,input().split())

ans=0
for i in range(k+1):
    for j in range(k+1):
        for h in range(k+1):
            if(i+j+h==s):
                ans+=1

print(ans)

Fixed submission:
k,s=map(int,input().split())

ans=0
for i in range(k+1):
    for j in range(k+1):
        if(0<=s-i-j<=k):
            ans+=1

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
k,s=map(int,input().split())

ans=0
for i in range(k+1):
    for j in range(k+1):
        for h in range(k+1):
            if(i+j+h==s):
                ans+=1

print(ans)

Fixed submission:
k,s=map(int,input().split())

ans=0
for i in range(k+1):
    for j in range(k+1):
        if(0<=s-i-j<=k):
            ans+=1

print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())

S = 0
for i in range(200001):
    S += n % 10
    n //= 10
    if n == 0:
        break

if S % 9 == 0:
    print("Yes")
else:
    print("No")


Fixed submission:
n = input()

S = 0
for i in range(len(n)):
    S += int(n[i])

if S % 9 == 0:
    print("Yes")
else:
    print("No")

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())

S = 0
for i in range(1, 200000):
    S += n % 10
    if n // 10  == 0:
        break
    else:
        n //= 10

if S % 9 == 0:
    print("Yes")
else:
    print("No")


Fixed submission:
n = input()

S = 0
for i in range(len(n)):
    S += int(n[i])

if S % 9 == 0:
    print("Yes")
else:
    print("No")
Buggy python submission (verdict: Runtime Error):
import fractions
from functools import reduce

n, m = map(int, input().split())
a = list(map( (lambda x: int(x)/2), input().split()))

div_num = [0 for _ in range(n)]
same = True

for i in range(n):
    tmp = a[i]
    while tmp%2 == 0:
        tmp //= 2
        div_num[i] += 1
    if div_num[0] != div_num[i]:
        same = False
        break

if same
    lcm = reduce(lambda x, y: (x*y)//fractions.gcd(x, y), a)
    print(int((m/lcm + 1)//2))
else:
    print(0)

Fixed submission:
import fractions
from functools import reduce

n, m = map(int, input().split())
a = list(map( (lambda x: int(x)//2), input().split()))

div_num = [0 for _ in range(n)]
same = True
for i in range(n):
    tmp = a[i]
    while tmp%2 == 0:
        tmp //= 2
        div_num[i] += 1
if len(set(div_num)) != 1:
    same = False

if same:
    lcm = reduce(lambda x, y: (x*y)//fractions.gcd(x, y), a)
    print(int((m/lcm + 1)//2))
else:
    print(0)

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

n, m = map(int, input().split())
a = list(map( (lambda x: int(x)/2), input().split()))

div_num = [0 for _ in range(n)]
same = True

for i in range(n):
    tmp = a[i]
    while tmp%2 == 0:
        tmp // = 2
        div_num[i] += 1
    if div_num[0] != div_num[i]:
        same = False
        break

if same
    lcm = reduce(lambda x, y: (x*y)//fractions.gcd(x, y), a)
    print(int((m/lcm + 1)//2))
else:
    print(0)

Fixed submission:
import fractions
from functools import reduce

n, m = map(int, input().split())
a = list(map( (lambda x: int(x)//2), input().split()))

div_num = [0 for _ in range(n)]
same = True
for i in range(n):
    tmp = a[i]
    while tmp%2 == 0:
        tmp //= 2
        div_num[i] += 1
if len(set(div_num)) != 1:
    same = False

if same:
    lcm = reduce(lambda x, y: (x*y)//fractions.gcd(x, y), a)
    print(int((m/lcm + 1)//2))
else:
    print(0)
Buggy python submission (verdict: Time Limit Exceeded):
import math

def comb(n, k, MOD, N):
    fact = [1]*(N+1)
    rfact = [1]*(N+1)
    r = 1
    for i in range(1, N+1):
        fact[i] = r = r * i % MOD
    rfact[N] = r = pow(fact[N], MOD-2, MOD)
    for i in range(N, 0, -1):
        rfact[i-1] = r = r * i % MOD
    return fact[n] * rfact[k] * rfact[n-k] % MOD

x, y = map(int, input().split())
mod = 10**9+7

diff = abs(x-y)
if (min(x, y) - diff) % 3 != 0:
    print(0)
else:
    count = (min(x, y) - diff) // 3
    print(comb(2*count+diff, count, mod, 10**7))

Fixed submission:
import math

def comb(n, k, MOD, N):
    fact = [1]*(N+1)
    rfact = [1]*(N+1)
    r = 1
    for i in range(1, N+1):
        fact[i] = r = r * i % MOD
    rfact[N] = r = pow(fact[N], MOD-2, MOD)
    for i in range(N, 0, -1):
        rfact[i-1] = r = r * i % MOD
    return fact[n] * rfact[k] * rfact[n-k] % MOD

x, y = map(int, input().split())
mod = 10**9+7

diff = abs(x-y)
if (min(x, y) - diff) % 3 != 0 or (min(x, y) - diff) < 0:
    print(0)
else:
    count = (min(x, y) - diff) // 3
    print(comb(2*count+diff, count, mod, 10**6))
Buggy python submission (verdict: Runtime Error):
import math
import sys

n = int(input())

low = sys.maxsize
a, b = 0, 0
for i in range(math.floor(math.sqrt(n))):
    if n%i == 0 and (i + n//i) <= low:
        a, b = i, n//i
        low = a + b
print(a+b-2)

Fixed submission:
n = int(input())

ans = n+1
for i in range(2, 10**6+1):
    if n%i == 0:
        ans = min(ans, i + n//i)
print(ans-2)
Buggy python submission (verdict: Runtime Error):
s = input()
k = int(input())

count = 0
change = False

for i in range(1, len(s)):
    if s[i-1] == s[i] and not change
        count += 1
        change = True
    else:
        change = False

count2 = 0
change2 = False
for i in range(2, len(s)):
    if s[i-1] == s[i] and not change2:
        count2 += 1
        change2 = True
    else:
        change2 = False


if len(s) == 1:
    print(k//2)
elif s[0] == s[-1] and not change:
    if change2:
        print((count+count2+1)*(k//2)+count*(k%2))
    else:
        print(count+(count2+1)*(k-1))
else:
    print(count*k)

Fixed submission:
s = input()
k = int(input())

count = 0
change = False
for i in range(1, len(s)):
    if s[i-1] == s[i] and not change:
        count += 1
        change = True
    else:
        change = False

count2 = 0
change2 = False
for i in range(2, len(s)):
    if s[i-1] == s[i] and not change2:
        count2 += 1
        change2 = True
    else:
        change2 = False

if len(s) == 1:
    print(k//2)
elif s[0] == s[-1] and not change:
    if change2:
        print((count+count2+1)*(k//2)+count)
    else:
        print(count+(count2+1)*(k-1))
else:
    print(count*k)

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

count = 0
change = False

for i in range(1, len(s)):
    if s[i-1] == s[i] and not change:
        count += 1
        change = True
    else:
        change = False
if s[0] == s[-1] and s[-2] != s[-1]:
    count += 1
    print(count*k-1)
else:
    print(count*k)

Fixed submission:
s = input()
k = int(input())

count = 0
change = False
for i in range(1, len(s)):
    if s[i-1] == s[i] and not change:
        count += 1
        change = True
    else:
        change = False

count2 = 0
change2 = False
for i in range(2, len(s)):
    if s[i-1] == s[i] and not change2:
        count2 += 1
        change2 = True
    else:
        change2 = False

if len(s) == 1:
    print(k//2)
elif s[0] == s[-1] and not change:
    if change2:
        print((count+count2+1)*(k//2)+count)
    else:
        print(count+(count2+1)*(k-1))
else:
    print(count*k)
Buggy python submission (verdict: Runtime Error):
h, w, a, b = map(int, input().split())

s = [[0 for _ in range(w)] for _ in range(h)]

num = ["0", "1"]
flag = True
for i in range(h):
    for j in range(w):
        if b <= i and flag:
            num.reverse()
            flag = False
        if j < a:
            s[i][j] = num[0]
        else:
            s[i][j] = num[1]


for row in s:
    print("".join(tmp))

Fixed submission:
h, w, a, b = map(int, input().split())

s = [[0 for _ in range(w)] for _ in range(h)]

num = [0, 1]
flag = True
for i in range(h):
    for j in range(w):
        if b <= i and flag:
            num.reverse()
            flag = False
        if j < a:
            s[i][j] = num[0]
        else:
            s[i][j] = num[1]


for row in s:
    tmp = list(map(str, row))
    print("".join(tmp))
Buggy python submission (verdict: Runtime Error):
n = int(input())
H = list(map(int, input().split()))
f = 0
if n ==1:
    print("Yes")
else:
    for i in range(1, n):
        if H[i+1] - H[i] < 0:
            H[i] -= 1
            if H[i-1] > H[i] or H[i+1] - H[i] < 0:
                f = 1
                break
    if f == 0:
        print("Yes")
    else:
        print("No")

Fixed submission:
n = int(input())
H = list(map(int, input().split()))
flag = 0

if n == 1:
    flag = 0
else:
    for i in range(n-1):
        idx = n-1-i
        if (H[idx-1] - H[idx]) == 1:
            H[idx-1] -= 1
        elif (H[idx-1] - H[idx]) > 1:
            flag = 1
            break

if flag == 0:
    print("Yes")
else:
    print("No")
Buggy python submission (verdict: Runtime Error):
def combination_list(n, mod=10**9+7):
    lst = [1]
    for i in range(1, n+1):
        lst.append(lst[-1] * (n+1-i) % mod * pow(i, mod-2, mod) % mod)
    return lst

n, k = map(int, input().split())
mod = 10**9+7

fst = combination_list(n-k+1, mod)
scd = combination_list(k-1, mod)

for i in range(1, k+1):
    print(fst[i] * scd[i-1] % mod)

Fixed submission:
n, k = map(int, input().split())
mod = 10**9+7

def cmb_table(n, mod):
    fac = [1] * (n+1)   # numerator
    finv = [1] * (n+1)   # denominator
    inv = [1] * (n+1)   # inverse of natural number
    inv[0] = 0
    for i in range(2, n+1):
        fac[i] = fac[i-1] * i % mod
        inv[i] = mod - inv[int(mod%i)] * (mod//i) % mod
        finv[i] = finv[i-1] * inv[i] % mod
    return fac, finv

def cmb(n, r, mod, fac, finv):
    if n < r:
        return 0
    if n < 0 or r < 0:
        return 0
    return int(fac[n] * finv[r] * finv[n-r] % mod)

a, b = cmb_table(n, mod)

for i in range(1, k+1):
    t1 = cmb(n-k+1, i, mod, a, b)
    t2 = cmb(k-1, i-1, mod, a, b)
    print(t1 * t2 % mod)
Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
A = list(map(int, input().split()))

for i in range(M):
  B, C = map(int, input().split())
  A = A + [C,]*B
  
A.sort(reverse=True)
sum = 0

for i in range(N):
  sum = sum + A[i]
  
print(sum)

Fixed submission:
N, M = map(int, input().split())
A = list(map(int, input().split()))

Nd = {}

for i in range(M):
  B, C = map(int, input().split())
  if C in Nd.keys():
    Nd[C] = Nd[C] + B
  else:
    Nd[C] = B
  
for a in A:
  if a in Nd.keys():
    Nd[a] = Nd[a] + 1
  else:
    Nd[a] = 1
    
Nd = sorted(Nd.items(), key=lambda x: -x[0]) # type=list
sum = 0

for key, val in Nd:
  if N >= val:
    sum = sum + key*val
    N = N-val
  else:
    sum = sum + key*N
    break;
  
print(sum)
Buggy python submission (verdict: Runtime Error):
from colloctions import Counter
from scipy import gcd
 
def sum_of_gcd(N):
  temp = [gcd(i, k) for i in range(1, N+1) for k in range(1, N+1)]
  counts = Counter(temp)
  return sum([gcd(i, c)*counts[c] for i in range(1, N+1) for c in counts.keys()])
 
print(sum_of_gcd(int(input())))

Fixed submission:
from scipy import gcd
from collections import Counter

def sum_of_gcd(N):
    temp = [gcd(i, k) for i in range(1, N+1) for k in range(1, N+1)]
    counts = Counter(temp)

    return sum([gcd(c, i)*counts[c] for i in range(1, N+1) for c in counts.keys()])

print(sum_of_gcd(int(input())))

Buggy python submission (verdict: Runtime Error):
from colloctions import Counter
import numpy as np

def sum_of_gcd(N):
  temp = [np.gcd(i, k) for i in range(1, N+1) for k in range(1, N+1)]
  counts = Counter(temp)
  return sum([np.gcd(i, c)*counts[c] for i in range(1, N+1) for c in counts.keys()])

print(sum_of_gcd(int(input())))

Fixed submission:
from scipy import gcd
from collections import Counter

def sum_of_gcd(N):
    temp = [gcd(i, k) for i in range(1, N+1) for k in range(1, N+1)]
    counts = Counter(temp)

    return sum([gcd(c, i)*counts[c] for i in range(1, N+1) for c in counts.keys()])

print(sum_of_gcd(int(input())))