Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))

compression_dict={a: ind+1 for ind, a in enumerate(sorted(set(A)|set(B)))}
A=[compression_dict[a] for a in A]
B=[compression_dict[a] for a in B]


SA=sorted(A)
SB=sorted(B)

for i in range(N):
    if SA[i]>SB[i]:
        print("No")
        sys.exit()

# BIT(BIT-indexed tree)
LEN=N

BIT=[0]*(LEN+1)# 1-indexedなtree

def update(v,w):# index vにwを加える
    while v<=LEN:
        BIT[v]+=w
        v+=(v&(-v))# 自分を含む大きなノードへ. たとえばv=3→v=4

def getvalue(v):# [1,v]の区間の和を求める
    ANS=0
    while v!=0:
        ANS+=BIT[v]
        v-=(v&(-v))# 自分より小さい2ベキのノードへ. たとえばv=3→v=2へ
    return ANS

for a in A:
    update(a,1)

BIT2=[0]*(LEN+1)# 1-indexedなtree

def update2(v,w):# index vにwを加える
    while v<=LEN:
        BIT2[v]+=w
        v+=(v&(-v))# 自分を含む大きなノードへ. たとえばv=3→v=4

def getvalue2(v):# [1,v]の区間の和を求める
    ANS=0
    while v!=0:
        ANS+=BIT2[v]
        v-=(v&(-v))# 自分より小さい2ベキのノードへ. たとえばv=3→v=2へ
    return ANS

for a in B:
    update2(a,1)

for i in range(N):
    a=A[i]
    b=B[i]

    update(a,-1)
    update2(b,-1)

    #print(getvalue(a),getvalue2(a),getvalue(b),getvalue2(b))

    if getvalue(a)<=getvalue2(a) and getvalue(b)<=getvalue2(b):
        update(a,1)
        update2(b,1)
    else:
        print("Yes")
        sys.exit()

print("No")
        



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

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))

compression_dict={a: ind+1 for ind, a in enumerate(sorted(set(A)|set(B)))}

SA=sorted(A)
SB=sorted(B)

for i in range(N):
    if SA[i]>SB[i]:
        print("No")
        sys.exit()

for i in range(N-1):
    if SB[i]>=SA[i+1]:
        print("Yes")
        sys.exit()

AB=[(B[i],A[i]) for i in range(N)]
AB.sort()

DICT={a:ind for ind,a  in enumerate(SA)}

Group=[i for i in range(N)]# グループ分け.Group[i]=jのときiとjは同じグループ

def find(x):# find(a)=find(b)のとき同じグループ
    while Group[x] != x:
        x=Group[x]
    return x

def Union(x,y):  # xとyが同じグループになるよう更新
    if find(x) != find(y):
        Group[find(y)]=Group[find(x)]=min(find(y),find(x))

for i in range(N):
    _,a=AB[i]

    Union(DICT[a],i)

if len(set([find(i) for i in range(N)]))==1:
    print("No")
else:
    print("Yes")
Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

S=input().strip()

from collections import deque
Q=deque(S)

ANS=0

count=0
while len(Q)>0 and Q[0]==">":
    count+=1
    Q.popleft()

ANS+=count*(count+1)//2
count=0

while len(Q)>0 and Q[-1]=="<":
    count+=1
    Q.pop()

ANS+=count*(count+1)//2


count=1
LIST=[]

for i in range(1,len(Q)):
    if Q[i]==Q[i-1]:
        count+=1
    else:
        LIST.append(count)
        count=1

LIST.append(count)

for i in range(0,len(LIST),2):
    s,t=sorted((LIST[i],LIST[i+1]))

    ANS+=t*(t+1)//2+s*(s-1)//2

print(ANS)


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

S=input().strip()

from collections import deque
Q=deque(S)

ANS=0

count=0
while len(Q)>0 and Q[0]==">":
    count+=1
    Q.popleft()

ANS+=count*(count+1)//2
count=0

while len(Q)>0 and Q[-1]=="<":
    count+=1
    Q.pop()

ANS+=count*(count+1)//2

if Q==deque():
    print(ANS)
    sys.exit()

Q=list(Q)

count=1
LIST=[]

for i in range(1,len(Q)):
    if Q[i]==Q[i-1]:
        count+=1
    else:
        LIST.append(count)
        count=1

LIST.append(count)

for i in range(0,len(LIST),2):
    s,t=sorted((LIST[i],LIST[i+1]))

    ANS+=t*(t+1)//2+s*(s-1)//2

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

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

A.sort()
F.sort(reverse=True)


MIN=0
MAX=max(A)*max(F)

while MIN!=MAX:
    mid=(MIN+MAX)//2
    score=0

    for i in range(N):
        if A[i]*F[i]>mid:
            score+=A[i]-mid//F[i]

    if score<=K:
        MAX=mid
    else:
        MIN=mid+1

print(MIN)


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

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

A.sort()
F.sort(reverse=True)


MIN=0
MAX=max(A)*max(F)

while MIN!=MAX:
    mid=(MIN+MAX)//2
    score=0

    for i in range(N):
        if A[i]*F[i]>mid:
            score+=A[i]-mid//F[i]

    if score<=K:
        MAX=mid
    else:
        MIN=mid+1

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

N,M,L=map(int,input().split())

E=[[] for i in range(N+1)]

for i in range(M):
    a,b,cost=map(int,input().split())

    E[a].append((b,cost))
    E[b].append((a,cost))


Q=int(input())
Query=[list(map(int,input().split())) for i in range(Q)]

ANS=[[(N+10,0) for i in range(N+1)] for j in range(N+1)]

from collections import deque
import heapq

for start in range(1,N+1):

    ANS[start][start]=(0,0)

    checking=[((0,0),start)]

    while checking:
        #print(checking)
        c,checktown=heapq.heappop(checking)
        h,cost0=c

        if ANS[start][checktown]<c:
            continue

        for to,cost in E[checktown]:
            
            if cost0+cost<=L and (h,cost0+cost)<ANS[start][to]:
                ANS[start][to]=(h,cost0+cost)
                heapq.heappush(checking,((h,cost0+cost),to))

            elif cost<=L and (h+1,cost)<ANS[start][to]:
                ANS[start][to]=(h+1,cost)
                heapq.heappush(checking,((h+1,cost),to))

for x,y in Query:
    if ANS[x][y][0]==N+10:
        print(-1)
    else:
        print(ANS[x][y][0])
    


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

N,M,L=map(int,input().split())

E=[[] for i in range(N+1)]

for i in range(M):
    a,b,cost=map(int,input().split())

    E[a].append((b,cost))
    E[b].append((a,cost))


Q=int(input())
Query=[list(map(int,input().split())) for i in range(Q)]

ANS=[[(N+10,0) for i in range(N+1)] for j in range(N+1)]

from collections import deque
import heapq

for start in range(1,N+1):

    ANS[start][start]=(0,0)

    checking=[((0,0),start)]

    while checking:
        #print(checking)
        c,checktown=heapq.heappop(checking)
        h,cost0=c

        if ANS[start][checktown]<c:
            continue

        for to,cost in E[checktown]:
            
            if cost0+cost<=L and (h,cost0+cost)<ANS[start][to]:
                ANS[start][to]=(h,cost0+cost)
                heapq.heappush(checking,((h,cost0+cost),to))

            elif cost<=L and (h+1,cost)<ANS[start][to]:
                ANS[start][to]=(h+1,cost)
                heapq.heappush(checking,((h+1,cost),to))

for x,y in Query:
    if ANS[x][y][0]==N+10:
        print(-1)
    else:
        print(ANS[x][y][0])
Buggy python submission (verdict: Time Limit Exceeded):
import math

N,L=map(int,input().split())
T=[int(input()) for i in range(N)]

ANSX=ANSY=0

for i in range(N-1):
    for j in range(i+1,N):
        ANSX+=math.cos((T[i]+T[j])*math.pi/L)*(N-(j-i+1))
        ANSY+=math.sin((T[i]+T[j])*math.pi/L)*(N-(j-i+1))

        ANSX+=math.cos((T[i]+T[j])*math.pi/L+math.pi)*(j-i-1)
        ANSY+=math.sin((T[i]+T[j])*math.pi/L+math.pi)*(j-i-1)

print(ANSX/(N*(N-1)*(N-2)//6),ANSY/(N*(N-1)*(N-2)//6))

Fixed submission:
import math

N,L=map(int,input().split())
T=[int(input()) for i in range(N)]

ANSX=ANSY=0

for i in range(N-1):
    for j in range(i+1,N):
        ANSX+=math.cos((T[i]+T[j])*math.pi/L)*(N-(j-i+1))
        ANSY+=math.sin((T[i]+T[j])*math.pi/L)*(N-(j-i+1))

        ANSX+=math.cos((T[i]+T[j])*math.pi/L+math.pi)*(j-i-1)
        ANSY+=math.sin((T[i]+T[j])*math.pi/L+math.pi)*(j-i-1)

print(ANSX/(N*(N-1)*(N-2)//6),ANSY/(N*(N-1)*(N-2)//6))
Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

N=int(input())
A=list(map(int,input().split()))

XOR=0
for a in A:
    XOR^=a

for i in range(N):
    A[i] &=~XOR
    
USED=[0]*60

for bi in range(60,-1,-1):
    for i in range(N):
        if USED[i]==0 and A[i] & (1<<bi)!=0:
            USED[i]=1
            useind=i
            break
    else:
        continue

    for i in range(N):
        if i==useind:
            continue
        if A[i] & (1<<bi)!=0:
            A[i]^=A[useind]
            
ANS=0
for a in A:
    ANS^=a

print(2*ANS+XOR)


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

N=int(input())
A=list(map(int,input().split()))

XOR=0
for a in A:
    XOR^=a

for i in range(N):
    A[i] &=~XOR
    
USED=[0]*N

for bi in range(60,-1,-1):
    for i in range(N):
        if USED[i]==0 and A[i] & (1<<bi)!=0:
            USED[i]=1
            useind=i
            break
    else:
        continue

    for i in range(N):
        if i==useind:
            continue
        if A[i] & (1<<bi)!=0:
            A[i]^=A[useind]
            
ANS=0
for a in A:
    ANS^=a

print(2*ANS+XOR)

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

N=int(input())
A=list(map(int,input().split()))

XOR=0
for a in A:
    XOR^=a

for i in range(N):
    A[i] &=~XOR
    
USED=[0]*60

for bi in range(60,-1,-1):
    for i in range(N):
        if USED[i]==0 and A[i] & (1<<bi)!=0:
            USED[i]=1
            useind=i
            break
    else:
        continue

    for i in range(N):
        if i==useind:
            continue
        if A[i] & (1<<bi)!=0:
            A[i]^=A[useind]
            print(A[i],A[useind])
            
ANS=0
for a in A:
    ANS^=a

print(2*ANS+XOR)


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

N=int(input())
A=list(map(int,input().split()))

XOR=0
for a in A:
    XOR^=a

for i in range(N):
    A[i] &=~XOR
    
USED=[0]*N

for bi in range(60,-1,-1):
    for i in range(N):
        if USED[i]==0 and A[i] & (1<<bi)!=0:
            USED[i]=1
            useind=i
            break
    else:
        continue

    for i in range(N):
        if i==useind:
            continue
        if A[i] & (1<<bi)!=0:
            A[i]^=A[useind]
            
ANS=0
for a in A:
    ANS^=a

print(2*ANS+XOR)
Buggy python submission (verdict: Time Limit Exceeded):
import sys
import copy
input = sys.stdin.readline

N = int(input())
A = sorted(map(int,input().split()),reverse=True)

USED=[0]*(1<<N)
USED[0]=1

for i in range(N):
    NOW=0
    k=0
    BUSED=copy.deepcopy(USED)
    for j in range(1<<i):
        while BUSED[k]==0:
            k+=1
        while USED[NOW]==1 or A[k]<=A[NOW]:
            NOW+=1

            if NOW==1<<N:
                print("No")
                sys.exit()

        USED[NOW]=1
        k+=1


print("Yes")

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

N = int(input())
A = sorted(map(int,input().split()),reverse=True)

USED=[0]*(1<<N)
USED[0]=1

for i in range(N):
    NOW=0
    k=0
    BUSED=copy.deepcopy(USED)
    for j in range(1<<i):
        while BUSED[k]==0:
            k+=1
        while USED[NOW]==1 or A[k]<=A[NOW]:
            NOW+=1

            if NOW==1<<N:
                print("No")
                sys.exit()

        USED[NOW]=1
        k+=1


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

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
BI=[(b,i) for i,b in enumerate(B)]

# Segment tree(1-indexed,再帰を使わないもの)

seg_el=1<<(N.bit_length())# Segment treeの台の要素数
SEG=[(0,0)]*(2*seg_el)# 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化

for i in range(N):
    SEG[i+seg_el]=BI[i]

for i in range(seg_el-1,0,-1):# 親の部分もupdate
    SEG[i]=max(SEG[i*2],SEG[i*2+1])

def update(n,x,seg_el):# A[n]をxへ更新（反映）
    i=n+seg_el
    SEG[i]=x
    i>>=1# 子ノードへ
    
    while i!=0:
        SEG[i]=max(SEG[i*2],SEG[i*2+1])
        i>>=1
        
def getvalues(l,r):# 区間[l,r)に関するmaxを調べる
    L=l+seg_el
    R=r+seg_el
    ANS=(0,0)

    while L<R:
        if L & 1:
            ANS=max(ANS , SEG[L])
            L+=1

        if R & 1:
            R-=1
            ANS=max(ANS , SEG[R])
        L>>=1
        R>>=1

    return ANS

ANS=0
while True:
    x,y=getvalues(0,N)
    if x==0:
        break
    if x<A[y]:
        print(-1)
        sys.exit()

    elif x==A[y]:
        update(y,(0,y),seg_el)

    else:
        B[y]-=B[(y+1)%N]+B[(y-1)%N]
        ANS+=1
        update(y,(B[y],y),seg_el)

print(ANS)
        

            


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

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
BI=[(b,i) for i,b in enumerate(B)]

# Segment tree(1-indexed,再帰を使わないもの)

seg_el=1<<(N.bit_length())# Segment treeの台の要素数
SEG=[(0,0)]*(2*seg_el)# 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化

for i in range(N):
    SEG[i+seg_el]=BI[i]

for i in range(seg_el-1,0,-1):# 親の部分もupdate
    SEG[i]=max(SEG[i*2],SEG[i*2+1])

def update(n,x,seg_el):# A[n]をxへ更新（反映）
    i=n+seg_el
    SEG[i]=x
    i>>=1# 子ノードへ
    
    while i!=0:
        SEG[i]=max(SEG[i*2],SEG[i*2+1])
        i>>=1
        
def getvalues(l,r):# 区間[l,r)に関するmaxを調べる
    L=l+seg_el
    R=r+seg_el
    ANS=(0,0)

    while L<R:
        if L & 1:
            ANS=max(ANS , SEG[L])
            L+=1

        if R & 1:
            R-=1
            ANS=max(ANS , SEG[R])
        L>>=1
        R>>=1

    return ANS

ANS=0
while True:
    x,y=getvalues(0,N)
    if x==0:
        break
    if x<A[y]:
        print(-1)
        sys.exit()

    elif x==A[y]:
        update(y,(0,y),seg_el)

    else:
        t=B[(y+1)%N]+B[(y-1)%N]
        if B[y]<t+A[y]:
            print(-1)
            sys.exit()
            
        q=(B[y]-A[y])//t
        ANS+=q
        B[y]-=t*q
        update(y,(B[y],y),seg_el)

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

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

x=sum(A)
import math
xr=math.ceil(math.sqrt(x))

LIST=[]
for i in range(1,xr+1):
    if x%i==0:
        LIST.append(i)
        LIST.append(x//i)


MIN=0
MAX=sum(A)
ANS=1
A.sort()

for l in LIST:
    count=0

    B=[a%l for a in A]
    B.sort()

    i=0
    j=N-1

    for i in range(N):
        if B[i]%l==0:
            continue
        else:
            count_temp=0
            while B[i]%l!=0:
                B[i]-=1
                count_temp+=1

            for t in range(count_temp):
                while B[j]%l==0:
                    j-=1
                B[j]+=1

        count+=count_temp


    if count<=K:
        ANS=max(ANS,l)

print(ANS)


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

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

x=sum(A)
import math
xr=math.ceil(math.sqrt(x))

LIST=[]
for i in range(1,xr+1):
    if x%i==0:
        LIST.append(i)
        LIST.append(x//i)

ANS=1

for l in LIST:
    count=0

    B=[a%l for a in A]
    B.sort()

    i=0
    j=N-1

    for i in range(N):
        if B[i]%l==0:
            continue
        else:
            count_temp=B[i]
            count+=count_temp
            B[i]=0

            while count_temp:
                while B[j]%l==0:
                    j-=1
                MINUS=min(count_temp,l-B[j])
                B[j]+=MINUS
                count_temp-=MINUS

    if count<=K:
        ANS=max(ANS,l)

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

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

X = A * 2

Nextcount = [-1] * (2 * (10**5+1))
Nextind = [-1]*N

for i,x in enumerate(X):
    if 0 <= Nextcount[x] < N:
        Nextind[Nextcount[x]] = i

    Nextcount[x] = i

Repeatcount=0
NOW = 0

Repeatcount+=Nextind[NOW]-NOW+1
NOW=(Nextind[NOW]+1)%N

while NOW!=0:
    Repeatcount+=Nextind[NOW]-NOW+1
    NOW=(Nextind[NOW]+1)%N
    

Rep=(N*K)%Repeatcount

from collections import Counter
C=Counter()
s=[]
for i in range(Rep):
    if X[i%N] in C:
        while X[i%N] in C:
            po=s.pop()
            C[po]-=1
            if C[po]==0:
                del C[po]

    else:
        s.append(X[i%N])
        C[X[i%N]]+=1

    #print(s,C)

print(*s)
        
            



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

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

X = A * 2

Nextcount = [-1] * (2 * (10**5+1))
Nextind = [-1]*N

for i,x in enumerate(X):
    if 0 <= Nextcount[x] < N:
        Nextind[Nextcount[x]] = i

    Nextcount[x] = i

Repeatcount=0
NOW = 0

Repeatcount+=Nextind[NOW]-NOW+1
NOW=(Nextind[NOW]+1)%N

while NOW!=0:
    Repeatcount+=Nextind[NOW]-NOW+1
    NOW=(Nextind[NOW]+1)%N
    

Rep=(N*K)%Repeatcount
NOW=0

while True:
    if Nextind[NOW]-NOW+1<Rep:
        Rep-=Nextind[NOW]-NOW+1
        NOW=(Nextind[NOW]+1)%N

    else:
        break
    
#print(Rep,NOW)

from collections import Counter
C=Counter()
s=[]
for i in range(Rep):
    if X[(NOW+i)%N] in C:
        while X[(NOW+i)%N] in C:
            po=s.pop()
            C[po]-=1
            if C[po]==0:
                del C[po]

    else:
        s.append(X[(NOW+i)%N])
        C[X[(NOW+i)%N]]+=1

    #print(s,C)

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

N,M = map(int,input().split())
mod = 998244353

FACT=[1]
for i in range(1,25*10**5+1):
    FACT.append(FACT[-1]*i%mod)

FACT_INV=[pow(FACT[-1],mod-2,mod)]
for i in range(25*10**5,0,-1):
    FACT_INV.append(FACT_INV[-1]*i%mod)

FACT_INV.reverse()

def Combi(a,b):
    if 0<=b<=a:
        return FACT[a]*FACT_INV[b]*FACT_INV[a-b]%mod
    else:
        return 0


ANS=Combi(M*3+N-1,N-1)

for i in range(M*2+1,M*3+1):
    k=M*3-i
    ANS=(ANS-N*Combi(k+(N-1)-1,N-2))%mod


for i in range(M+1,N+1):
    if (M*3-i)%2==1:
        continue
    k=(M*3-i)//2
    ANS=(ANS-Combi(N,i)*Combi(k+N-1,N-1))%mod

print(ANS)



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

N,M = map(int,input().split())
mod = 998244353

FACT=[1]
for i in range(1,4*10**6+1):
    FACT.append(FACT[-1]*i%mod)

FACT_INV=[pow(FACT[-1],mod-2,mod)]
for i in range(4*10**6,0,-1):
    FACT_INV.append(FACT_INV[-1]*i%mod)

FACT_INV.reverse()

def Combi(a,b):
    if 0<=b<=a:
        return FACT[a]*FACT_INV[b]*FACT_INV[a-b]%mod
    else:
        return 0


ANS=Combi(M*3+N-1,N-1)

for i in range(M*2+1,M*3+1):
    k=M*3-i
    ANS=(ANS-N*Combi(k+(N-1)-1,N-2))%mod


for i in range(M+1,N+1):
    if (M*3-i)%2==1:
        continue
    k=(M*3-i)//2
    ANS=(ANS-Combi(N,i)*Combi(k+N-1,N-1))%mod

print(ANS)

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

N,M = map(int,input().split())
mod = 998244353

FACT=[1]
for i in range(1,2*10**6+1):
    FACT.append(FACT[-1]*i%mod)

FACT_INV=[pow(FACT[-1],mod-2,mod)]
for i in range(2*10**6,0,-1):
    FACT_INV.append(FACT_INV[-1]*i%mod)

FACT_INV.reverse()

def Combi(a,b):
    if 0<=b<=a:
        return FACT[a]*FACT_INV[b]*FACT_INV[a-b]%mod
    else:
        return 0


ANS=Combi(M*3+N-1,N-1)

for i in range(M*2+1,M*3+1):
    k=M*3-i
    ANS=(ANS-N*Combi(k+(N-1)-1,N-2))%mod


for i in range(M+1,N+1):
    if (M*3-i)%2==1:
        continue
    k=(M*3-i)//2
    ANS=(ANS-Combi(N,i)*Combi(k+N-1,N-1))%mod

print(ANS)



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

N,M = map(int,input().split())
mod = 998244353

FACT=[1]
for i in range(1,4*10**6+1):
    FACT.append(FACT[-1]*i%mod)

FACT_INV=[pow(FACT[-1],mod-2,mod)]
for i in range(4*10**6,0,-1):
    FACT_INV.append(FACT_INV[-1]*i%mod)

FACT_INV.reverse()

def Combi(a,b):
    if 0<=b<=a:
        return FACT[a]*FACT_INV[b]*FACT_INV[a-b]%mod
    else:
        return 0


ANS=Combi(M*3+N-1,N-1)

for i in range(M*2+1,M*3+1):
    k=M*3-i
    ANS=(ANS-N*Combi(k+(N-1)-1,N-2))%mod


for i in range(M+1,N+1):
    if (M*3-i)%2==1:
        continue
    k=(M*3-i)//2
    ANS=(ANS-Combi(N,i)*Combi(k+N-1,N-1))%mod

print(ANS)
Buggy python submission (verdict: Runtime Error):
L,R=map(int,input().split())
mod=2019

if R>=L+2020:
    print(0)
else:
    D=list(range(L,R+1))

    L=len(D)

    ANS=1<<40

    for i in range(L-1):
        for j in range(i+1,L):
            ANS=min(ANS,D[i]*D[j]%mod)

print(ANS)
            

Fixed submission:
L,R=map(int,input().split())
mod=2019

if R>=L+2020:
    print(0)
else:
    D=list(range(L,R+1))

    L=len(D)

    ANS=1<<40

    for i in range(L-1):
        for j in range(i+1,L):
            ANS=min(ANS,D[i]*D[j]%mod)

    print(ANS)
Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

N,A,B,C,D=map(int,input().split())
S=input().strip()

BLOCK=[0]*N
OPEN=[0]*N

for i in range(1,N):
    if S[i]=="#" and S[i-1]=="#":
        BLOCK[i]=1

for i in range(2,N):
    if S[i]==S[i-1]==S[i-2]==".":
        OPEN[i]=1

RIGHT_A=N-1
for i in range(A,N):
    if BLOCK[i]==1:
        RIGHT_A=i
        break

RIGHT_B=N-1
for i in range(B,N):
    if BLOCK[i]==1:
        RIGHT_B=i
        break

if C<=RIGHT_A+1 and D<=RIGHT_B+1:
    if C<D:
        print("Yes")
    if RIGHT_A==RIGHT_B:
        for j in range(B+1,D+3):
            if OPEN[j]==1:
                print("Yes")
                sys.exit()

        else:
            print("No")
                
    else:
      print("Yes")
else:
    print("No")


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

N,A,B,C,D=map(int,input().split())
S=input().strip()
S+="#####"

A-=1
B-=1
C-=1
D-=1

if C<D:
    while B!=D or  A!=C:
        #print(A,B)
        if B!=D and S[B+1]==".":
            B+=1
        elif B!=D and S[B+2]==".":
            B+=2
        elif B!=D and S[B+1]=="#" and S[B+2]=="#":
            print("No")
            sys.exit()


        if A!=C and S[A+1]==".":
            A+=1
        elif A!=C and S[A+2]==".":
            A+=2
        elif A!=C and S[A+1]=="#" and S[A+2]=="#":
            print("No")
            sys.exit()

    print("Yes")

else:
    while A<B:
            
        if S[A+1]=="." and A+1!=B:
            A+=1
        elif S[A+2]=="." and A+2!=B:
            A+=2
        elif S[A+1]=="#" and S[A+2]=="#":
            print("No")
            sys.exit()

        if A+1==B or (A+2==B and S[A+1]=="#"):
            break

    while True:
        if A+1==B and S[B+1]==".":
            A+=2
            break

        if S[B+1]==".":
            B+=1
        elif S[B+2]==".":
            B+=2
        else:
            print("No")
            sys.exit()

        if S[A+1]==".":
            A+=1
        elif S[A+2]==".":
            A+=2

        if B>D:
            print("No")
            sys.exit()

    
    while B!=D or  A!=C:
        
        if A!=C and S[A+1]==".":
            A+=1
        elif A!=C and S[A+2]==".":
            A+=2
        elif A!=C and S[A+1]=="#" and S[A+2]=="#":
            print("No")
            sys.exit()
            
        if B!=D and S[B+1]==".":
            B+=1
        elif B!=D and S[B+2]==".":
            B+=2
        elif B!=D and S[B+1]=="#" and S[B+2]=="#":
            print("No")
            sys.exit()




    print("Yes")