input stringlengths 20 127k | target stringlengths 20 119k | problem_id stringlengths 6 6 |
|---|---|---|
import sys
sys.setrecursionlimit(10**7)
import math
def cmb(n, r):
if n - r < r: r = n - r
if r == 0: return 1
if r == 1: return n
numerator = [n - r + k + 1 for k in range(r)]
denominator = [k + 1 for k in range(r)]
for p in range(2,r+1):
pivot = denominator[p - 1]
if pivot > 1:
offset = (n - r) % p
for k in range(p-1,r,p):
numerator[k - offset] /= pivot
denominator[k] /= pivot
result = 1
for k in range(r):
if numerator[k] > 1:
result *= int(numerator[k])
return result
z = 10**9+7
X, Y = list(map(int, input().split()))
x = (-X+2*Y)/3
y = (2*X-Y)/3
if x.is_integer() and y.is_integer() and x>=0 and y>=0:
x = int(x)
y = int(y)
maximam = max(x,y)
minimam = min(x,y)
print((cmb(x+y,minimam)%z))
else:
print((0)) | import sys
sys.setrecursionlimit(10**7)
import math
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
X, Y = list(map(int, input().split()))
x = (-X+2*Y)/3
y = (2*X-Y)/3
if x.is_integer() and y.is_integer() and x>=0 and y>=0:
x = int(x)
y = int(y)
maximam = max(x,y)
minimam = min(x,y)
mod = 10**9+7 #出力の制限
N = x+y
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 )
print((cmb(x+y,minimam,mod)))
else:
print((0)) | p02862 |
mod = int(1e9 + 7)
def powmod(a, b):
ans = 1
while(b):
if(b&1): ans = ans*a%mod
a = a*a%mod
b >>= 1
return ans
x, y = list(map(int,input().split()))
if(2*x < y or 2*y < x or (2*x-y)%3 or (2*y-x)%3): print((0))
else:
x, y = (2*x-y)//3, (2*y-x)//3
#print(x,y)
fac = [0 for i in range(x+y+1)]
inv = [0 for i in range(x+y+1)]
fac[0] = 1
for i in range(1,x+y+1):
fac[i] = fac[i-1]*i%mod
inv[x+y] = powmod(fac[x+y],mod-2)
for i in range(x+y-1,-1,-1):
inv[i] = inv[i+1]*(i+1)%mod
ans = fac[x+y]*inv[x]*inv[y]%mod
print(ans) | mod = int(1e9 + 7)
x, y = list(map(int,input().split()))
if(2*x < y or 2*y < x or (2*x-y)%3 or (2*y-x)%3): print((0))
else:
x, y = (2*x-y)//3, (2*y-x)//3
#print(x,y)
fac = [0 for i in range(x+y+1)]
fac[0] = 1
for i in range(1,x+y+1):
fac[i] = fac[i-1]*i%mod
ans = fac[x+y]*pow(fac[x],mod-2,mod)*pow(fac[y],mod-2,mod)%mod
print(ans) | p02862 |
# encoding:utf-8
import copy
import random
import bisect #bisect_left これで二部探索の大小検索が行える
import fractions #最小公倍数などはこっち
import math
import sys
import collections
mod = 10**9+7
#modに対応して高速なコンビネーションが求められる
# 階乗 & 逆元計算
n = 10 ** 6
factorial = [1]
inverse = [1]
for i in range(1, n+2):
factorial.append(factorial[-1] * i % mod)
inverse.append(pow(factorial[-1], mod-2, mod))
def combinations_count(n,r):
if n-r < 0:
return 0
return factorial[n]*inverse[r]*inverse[n-r]%mod
d = collections.deque()
def LI(): return list(map(int, sys.stdin.readline().split()))
X,Y = LI()
if (X + Y) % 3 != 0:
ans = 0
else:
m = int(X * 2 / 3 - Y / 3)
n = int(Y * 2 / 3 - X / 3)
# print(m,n)
ans = combinations_count(m + n, n)
print(ans)
| # encoding:utf-8
import copy
import random
import bisect #bisect_left これで二部探索の大小検索が行える
import fractions #最小公倍数などはこっち
import math
import sys
import collections
mod = 10**9+7
#modに対応して高速なコンビネーションが求められる
# 階乗 & 逆元計算
d = collections.deque()
def LI(): return list(map(int, sys.stdin.readline().split()))
X,Y = LI()
if (X + Y) % 3 != 0:
ans = 0
else:
n = 10 ** 6
factorial = [1]
inverse = [1]
for i in range(1, n+2):
factorial.append(factorial[-1] * i % mod)
inverse.append(pow(factorial[-1], mod-2, mod))
def combinations_count(n,r):
if n-r < 0:
return 0
return factorial[n]*inverse[r]*inverse[n-r]%mod
m = int(X * 2 / 3 - Y / 3)
n = int(Y * 2 / 3 - X / 3)
if (X+Y) / 3 > X or (X + Y) / 3 > Y or m < 0 or n < 0:
ans = 0
else:
ans = combinations_count((X + Y)//3, n)
print(ans)
| p02862 |
x,y=list(map(int,input().split()))
if (2*x-y)%3!=0 or (2*x-y)<0:
print((0))
exit()
if (2*y-x)%3!=0 or (2*y-x)<0:
print((0))
exit()
p=int((2*x-y)/3)
q=int((2*y-x)/3)
M=2*(10**6)
Mod=10**9+7
fac=[0]*M
finv=[0]*M
inv=[0]*M
def COMinit():
fac[0]=fac[1]=1
finv[0]=finv[1]=1
inv[1]=1
for i in range(2,M):
fac[i]=(fac[i-1]*i%Mod)%Mod
inv[i]=Mod-inv[Mod%i]*(Mod//i) %Mod
finv[i]=(finv[i-1]*inv[i]%Mod)%Mod
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)%Mod
COMinit()
print((COM(p+q,p))) | x,y=list(map(int,input().split()))
if (2*x-y)%3!=0 or (2*x-y)<0:
print((0))
exit()
if (2*y-x)%3!=0 or (2*y-x)<0:
print((0))
exit()
p=int((2*x-y)/3)
q=int((2*y-x)/3)
M=p+q+2
Mod=10**9+7
fac=[0]*M
finv=[0]*M
inv=[0]*M
def COMinit():
fac[0]=fac[1]=1
finv[0]=finv[1]=1
inv[1]=1
for i in range(2,M):
fac[i]=(fac[i-1]*i%Mod)%Mod
inv[i]=Mod-inv[Mod%i]*(Mod//i) %Mod
finv[i]=(finv[i-1]*inv[i]%Mod)%Mod
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)%Mod
COMinit()
print((COM(p+q,p))) | p02862 |
x, y = list(map(int, input().split()))
from operator import mul
from functools import reduce
def cmb(n, r, mod):
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 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
if (x+y) % 3 != 0:
ans = 0
else:
a = (x + y)//3
b = x-a
if x-a <0 or y-a <0:
ans = 0
else:
mod = 10**9+7 #出力の制限
N = a+b
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 )
ans = cmb(a, b, mod)
print((int(ans)))
| x, y = list(map(int, input().split()))
def cmb(n, r, mod):
from operator import mul
from functools import reduce
N = n + r
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
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)
if (r<0 or r>n):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
if (x+y) % 3 != 0:
ans = 0
else:
a = (x + y)//3
b = x-a
if x-a <0 or y-a <0:
ans = 0
else:
mod = 10**9+7 #出力の制限
ans = cmb(a, b, mod)
print((int(ans)))
| p02862 |
def make_tables(m):
fac=[1,1]
finv=[1,1]
inv=[0,1]
for i in range(2,m+1):
fac.append((fac[-1]*i)%mod)
inv.append((-inv[mod%i]*(mod//i))%mod)
finv.append(finv[i-1]*inv[i]%mod)
return fac,finv
def calc_nCk(n,k,fac,finv):
if n<k or (n<0 or k<0):
return 0
# k=min(k,n-k)
return fac[n]*(finv[k]*finv[n-k]%mod)%mod
x,y=list(map(int,input().split()))
mod=10**9+7
n=(y-0.5*x)/1.5
if int(n)!=n:
print((0))
else:
m=(y+x)//3
l=int(n)
fac,finv=make_tables(m)
ans = calc_nCk(m,l,fac,finv)
print(ans) | def nCk(n,k):
if n<k or (n<0 or k<0):
return 0
#k=min(k,n-k)
num,denum=1,1
for i in range(k):
num=num*(n-i)%mod
denum=denum*(i+1)%mod
return num*pow(denum,mod-2,mod)%mod
x,y=list(map(int,input().split()))
mod=10**9+7
n=(y-0.5*x)/1.5
if int(n)!=n:
print((0))
else:
m=(y+x)//3
l=int(n)
print((nCk(m,l))) | p02862 |
#!/usr/bin/env python3
from functools import reduce
x, y = list(map(int, input().split()))
mod = 10**9 + 7
def cmb(n, r, m):
def mul(a, b):
return a * b % m
r = min(n - r, r)
if r == 0:
return 1
over = reduce(mul, list(range(n, n - r, -1)))
under = reduce(mul, list(range(1, r + 1)))
return (over * pow(under, m - 2, m))%m
r = abs(x - y)
l = (min(x, y) - r) // 3
r += l
if l*2+r*1 in (x,y) and l >= 0:
print((cmb(r + l, l, mod)))
else:
print((0))
| #!/usr/bin/env python3
from functools import reduce
x, y = list(map(int, input().split()))
mod = 10**9 + 7
def cmb(n, r, m):
def mul(a, b):
return a * b % m
r = min(n - r, r)
if r == 0:
return 1
over = reduce(mul, list(range(n, n - r, -1)))
under = reduce(mul, list(range(1, r + 1)))
return (over * pow(under, m - 2, m))%m
r = abs(x - y)
l = (min(x, y) - r) // 3
r += l
if (x+y)%3 < 1 and l >= 0:
print((cmb(r + l, l, mod)))
else:
print((0))
| p02862 |
LARGE = 10 ** 9 + 7
def solve(x, y):
if (x + y) % 3 != 0:
return 0
z = (x + y) // 3
if x < z or y < z:
return 0
# zC(x-z)
r = min(x - z, y - z)
res = 1
for i in range(r):
res *= z - i
res *= pow(i + 1, LARGE - 2, LARGE)
res %= LARGE
return res
def main():
x, y = list(map(int, input().split()))
res = solve(x, y)
print(res)
def test():
assert solve(3, 3) == 2
assert solve(2, 2) == 0
assert solve(999999, 999999) == 151840682
if __name__ == "__main__":
test()
main()
| LARGE = 10 ** 9 + 7
def solve(x, y):
if (x + y) % 3 != 0:
return 0
z = (x + y) // 3
if x < z or y < z:
return 0
# zC(x-z)
r = min(x - z, y - z)
res = 1
for i in range(r):
res *= z - i
res *= pow(i + 1, LARGE - 2, LARGE)
res %= LARGE
return res
def main():
x, y = list(map(int, input().split()))
res = solve(x, y)
print(res)
def test():
assert solve(3, 3) == 2
assert solve(2, 2) == 0
assert solve(999999, 999999) == 151840682
if __name__ == "__main__":
# test()
main()
| p02862 |
x,y = list(map(int,input().split()))
if (x+y) % 3 != 0:
print((0))
elif x < 0 or y < 0:
print((0))
elif x/y > 2 or y/x > 2:
print((0))
else:
n = (x+y) // 3
m = x - n
mod = 10**9 + 7
def inv(x):
y = 1
while x != 1:
y *= mod//x + 1
y %= mod
x -= mod%x
return y
#print(inv(5))
ans = 1
for i in range(m):
ans *= (n-i)
ans %= mod
ans *= inv(m-i)
ans %= mod
#print(n,m)
print(ans) | #17:23
x,y = list(map(int,input().split()))
if (x+y) % 3 != 0:
print((0))
elif x*2 < y or y*2 < x:
print((0))
else:
a = (x + y) // 3
b = y - a
mod = 10 ** 9 + 7
def inv(x):
y = 1
while x != 1:
y *= mod // x + 1
y %= mod
x -= mod % x
return y
ans = 1
for i in range(b):
ans *= a - i
ans %= mod
ans *= inv(b-i)
ans %= mod
print(ans) | p02862 |
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
N = 10**6 #出力の制限
mod = 10**9+7
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 = list(map(int, input().split()))
n = 2 * Y - X
m = 2 * X - Y
r = 1
if n % 3 != 0:
r = 0
elif m % 3 != 0:
r = 0
else:
r = cmb(n//3+m//3,n//3,mod)
print(r) | mod = 10 ** 9 + 7 # mod素数
def nCr(n, r, mod):
ret = [1]*(r+1)
for i in range(1, r+1):
ret[i] = (ret[i-1] * (n-i+1) * pow(i,mod-2,mod)) % mod
return ret
X,Y=list(map(int,input().split()))
x,y = 2*X-Y, 2*Y-X
if x<0 or y<0 or x%3!=0 or y%3!=0:
ret=0
else:
x,y=x//3,y//3
nCrl = nCr(x+y, min(x,y), mod)
ret=nCrl[min(x,y)]
print(ret) | p02862 |
#coding:utf-8
import bisect
import sys
sys.setrecursionlimit(10**6)
write = sys.stdout.write
dbg = lambda *something : print(*something) if DEBUG else 0
DEBUG = True
def com(a, b, p):
if a < b or a < 0 or b < 0:
return 0
fac = [1]*(a+1)
inv = [1]*(a+1)
finv = [1]*(a+1)
for i in range(2, a+1):
fac[i] = fac[i-1] * i % p
inv[i] = p - (inv[p%i] * (p//i) )% p
finv[i] = finv[i-1] * inv[i] % p
return fac[a] * (finv[b] * finv[a - b] % p) % p
def main(given = sys.stdin.readline):
input = lambda : given().rstrip()
LMIIS = lambda : list(map(int,input().split()))
II = lambda : int(input())
XLMIIS = lambda x : [LMIIS() for _ in range(x)]
x, y = LMIIS()
if (x+y)%3!=0:
print(0)
exit()
n = (x+y)//3
if 0 > x-n or 0 > y-n:
print(0)
exit()
m = min(x-n,y-n)
mod = 10**9 + 7
print(com(n, m, mod))
if __name__ == '__main__':
main()
| #coding:utf-8
import bisect
import sys
sys.setrecursionlimit(10**6)
write = sys.stdout.write
dbg = lambda *something : print(*something) if DEBUG else 0
DEBUG = True
def main(given = sys.stdin.readline):
input = lambda : given().rstrip()
LMIIS = lambda : list(map(int,input().split()))
II = lambda : int(input())
XLMIIS = lambda x : [LMIIS() for _ in range(x)]
x, y = LMIIS()
if (x+y)%3!=0:
print(0)
exit()
n = (x+y)//3
if 0 > x-n or 0 > y-n:
print(0)
exit()
m = min(x-n,y-n)
mod = 10**9 + 7
a = 1
b = 1
for i in range(n - m + 1, n+1):
a = a * i % mod
for i in range(1, m + 1):
b = b * i % mod
print(a * pow(b, mod - 2, mod) % mod)
if __name__ == '__main__':
main()
| p02862 |
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
x,y = list(map(int,input().split()))
mod = 10**9+7
division = (x+y)//3
if (x+y)%3!=0:
print((0))
exit()
mod = 10**9+7
#combを求める前処理 O(log division)
g1 = [1, 1] #元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
for i in range( 2, division + 1 ):
g1.append( ( g1[-1] * i ) % mod )
inverse.append( pow(i,mod-2,mod) )
g2.append( (g2[-1] * inverse[-1]) % mod )
r = min(x,y)-division
ans = cmb(division,r,mod)
print(ans) | def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
x,y = list(map(int,input().split()))
if (x+y)%3!=0:
print((0))
exit()
mod = 10**9+7
division = (x+y)//3
#combを求める前処理（階乗とその逆数）
g1 = [1, 1] #元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
for i in range( 2, division + 1 ):
g1.append( ( g1[-1] * i ) % mod )
inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
g2.append( (g2[-1] * inverse[-1]) % mod )
#################################
r = min(x,y)-division
ans = cmb(division,r,mod)
print(ans) | p02862 |
MOD=10**9+7
x , y = list(map(int, input().split()))
a=(2*x-y)//3
b=(2*y-x)//3
if 2*a+b!=x:
print((0))
exit()
factorial = [1]
inverse = [1]
n=a+b
r=a
for i in range(1, n+2):
factorial.append(factorial[-1] * i % MOD)
inverse.append(pow(factorial[-1], MOD - 2, MOD))
def combi(n, r):
if n < r or r < 0:
return 0
elif r == 0:
return 1
return factorial[n] * inverse[r] * inverse[n - r] % MOD
ans = combi(n,r)
print(ans)
| N=10**9+7
x , y = list(map(int, input().split()))
a=(2*x-y)//3
b=(2*y-x)//3
if 2*a+b!=x:
print((0))
exit()
n=a+b
r=a
def fac(n,r,N):
ans=1
for i in range(r):
ans=ans*(n-i)%N
return ans
def combi(n,r,N):
if n<r or n<0 or r<0:
ans = 0
return ans
r= min(r, n-r)
ans = fac(n,r,N)*pow(fac(r,r,N),N-2,N)%N
return ans
ans = combi(n,r,N)
print(ans)
| p02862 |
def solve(x, y):
if (x + y) % 3 != 0:
return 0
n = (x + y) // 3
r = min((2 * y - x) // 3, (2 * x - y) // 3)
return cmb(n, r, mod)
_x, _y = list(map(int, input().split()))
mod = 10 ** 9 + 7
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
for i in range(2, _x + _y + 1):
g1.append((g1[-1] * i) % mod)
inverse.append((- inverse[mod % i] * (mod // i)) % mod)
g2.append((g2[-1] * inverse[-1]) % mod)
def cmb(n, r, mod):
if r < 0 or r > n:
return 0
r = min(r, n - r)
return g1[n] * g2[r] * g2[n - r] % mod
print((solve(_x, _y)))
| def solve(x, y):
if (x + y) % 3 != 0:
return 0
n = (x + y) // 3
r = min((2 * y - x) // 3, (2 * x - y) // 3)
return cmb(n, r, mod)
_x, _y = list(map(int, input().split()))
mod = 10 ** 9 + 7
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
for i in range(2, max(_x, _y) + 1):
g1.append((g1[-1] * i) % mod)
inverse.append((- inverse[mod % i] * (mod // i)) % mod)
g2.append((g2[-1] * inverse[-1]) % mod)
def cmb(n, r, mod):
if r < 0 or r > n:
return 0
r = min(r, n - r)
return g1[n] * g2[r] * g2[n - r] % mod
print((solve(_x, _y)))
| p02862 |
# 入力が10**5とかになったときに100ms程度早い
import sys
read = sys.stdin.readline
def read_ints():
return list(map(int, read().split()))
def read_a_int():
return int(read())
def read_matrix(H):
'''
H is number of rows
'''
return [list(map(int, read().split())) for _ in range(H)]
def read_map(H):
'''
H is number of rows
文字列で与えられた盤面を読み取る用
'''
return [read()[:-1] for _ in range(H)]
def read_col(H, n_cols):
'''
H is number of rows
n_cols is number of cols
A列、B列が与えられるようなとき
'''
ret = [[] for _ in range(n_cols)]
for _ in range(H):
tmp = list(map(int, read().split()))
for col in range(n_cols):
ret[col].append(tmp[col])
return ret
MOD = 10**9 + 7
X, Y = read_ints()
if (X + Y) % 3 != 0: # !=0
print((0))
exit()
pascal_depth = int((X + Y) / 3) # パスカルの三角形に当たるn
x, y = int((X + Y) * 2 / 3), (X + Y) / 3
pascal_k = x - X # 端からいくつずれているか
if pascal_k > pascal_depth / 2:
pascal_k = pascal_depth - pascal_k
# ans = 1
# # for k in range(int(pascal_k), 0, -1):
# # ans *= pascal_depth
# # # print(ans)
# # pascal_depth -= 1
# # if ans > MOD:
# # ans %= MOD
# # for k in range(int(pascal_k), 0, -1):
# # フェルマーの少定理jを使ってみる
# for i in range(1, int(pascal_depth) + 1):
# ans *= i
# if ans > MOD:
# ans %= MOD
# from math import factorial
# # k_fact = factorial(pascal_k)
# k_fact = 1
# # k_fact
# for i in range(1, pascal_k + 1):
# k_fact *= i
# if k_fact > MOD:
# k_fact %= MOD
# ans *= k_fact**(MOD - 2) % MOD
# # nk_fact = factorial(pascal_depth - pascal_k)
# nk_fact = 1
# for i in range(1, int(pascal_depth - pascal_k) + 1):
# nk_fact *= i
# if nk_fact > MOD:
# nk_fact %= MOD
# ans *= nk_fact**(MOD - 2) % MOD
def cmb(n, r, mod):
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 # 出力の制限
N = pascal_depth
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
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)
a = cmb(pascal_depth, pascal_k, mod)
print(a)
| # 入力が10**5とかになったときに100ms程度早い
import sys
read = sys.stdin.readline
def read_ints():
return list(map(int, read().split()))
def read_a_int():
return int(read())
def read_matrix(H):
'''
H is number of rows
'''
return [list(map(int, read().split())) for _ in range(H)]
def read_map(H):
'''
H is number of rows
文字列で与えられた盤面を読み取る用
'''
return [read()[:-1] for _ in range(H)]
def read_col(H, n_cols):
'''
H is number of rows
n_cols is number of cols
A列、B列が与えられるようなとき
'''
ret = [[] for _ in range(n_cols)]
for _ in range(H):
tmp = list(map(int, read().split()))
for col in range(n_cols):
ret[col].append(tmp[col])
return ret
MOD = 10**9 + 7
X, Y = read_ints()
if (X + Y) % 3 != 0: # !=0
print((0))
exit()
pascal_depth = int((X + Y) / 3) # パスカルの三角形に当たるn
x, y = int((X + Y) * 2 / 3), (X + Y) / 3
pascal_k = x - X # 端からいくつずれているか
if pascal_k > pascal_depth / 2:
pascal_k = pascal_depth - pascal_k
def cmb(n, r, mod):
if (r < 0 or r > n):
return 0
r = min(r, n - r)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
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)
return g1[n] * g2[r] * g2[n - r] % mod
a = cmb(pascal_depth, pascal_k, MOD)
print(a)
| p02862 |
# 入力が10**5とかになったときに100ms程度早い
import sys
read = sys.stdin.readline
def read_ints():
return list(map(int, read().split()))
def read_a_int():
return int(read())
def read_matrix(H):
'''
H is number of rows
'''
return [list(map(int, read().split())) for _ in range(H)]
def read_map(H):
'''
H is number of rows
文字列で与えられた盤面を読み取る用
'''
return [read()[:-1] for _ in range(H)]
def read_col(H, n_cols):
'''
H is number of rows
n_cols is number of cols
A列、B列が与えられるようなとき
'''
ret = [[] for _ in range(n_cols)]
for _ in range(H):
tmp = list(map(int, read().split()))
for col in range(n_cols):
ret[col].append(tmp[col])
return ret
MOD = 10**9 + 7
X, Y = read_ints()
if (X + Y) % 3 != 0: # !=0
print((0))
exit()
pascal_depth = int((X + Y) / 3) # パスカルの三角形に当たるn
x, y = int((X + Y) * 2 / 3), (X + Y) / 3
pascal_k = x - X # 端からいくつずれているか
if pascal_k > pascal_depth / 2:
pascal_k = pascal_depth - pascal_k
def cmb(n, r, mod):
if (r < 0 or r > n):
return 0
r = min(r, n - r)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
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)
return g1[n] * g2[r] * g2[n - r] % mod
a = cmb(pascal_depth, pascal_k, MOD)
print(a)
| # 入力が10**5とかになったときに100ms程度早い
import sys
read = sys.stdin.readline
def read_ints():
return list(map(int, read().split()))
def read_a_int():
return int(read())
def read_matrix(H):
'''
H is number of rows
'''
return [list(map(int, read().split())) for _ in range(H)]
def read_map(H):
'''
H is number of rows
文字列で与えられた盤面を読み取る用
'''
return [read()[:-1] for _ in range(H)]
def read_col(H, n_cols):
'''
H is number of rows
n_cols is number of cols
A列、B列が与えられるようなとき
'''
ret = [[] for _ in range(n_cols)]
for _ in range(H):
tmp = list(map(int, read().split()))
for col in range(n_cols):
ret[col].append(tmp[col])
return ret
MOD = 10**9 + 7
X, Y = read_ints()
if (X + Y) % 3 != 0 or Y / X > 2 or Y / X < 1 / 2: # !=0
print((0))
exit()
pascal_depth = int((X + Y) / 3) # パスカルの三角形に当たるn
x = ((X + Y) * 2) // 3
pascal_k = x - X # 端からいくつずれているか
def combination(n, r, mod=MOD):
r = min(r, n - r)
nf = rf = 1
for i in range(r):
nf = nf * (n - i) % mod
rf = rf * (i + 1) % mod
return nf * pow(rf, mod - 2, mod) % mod
# def com(n, k, mod):
# if k == 0:
# return 1
# s = n
# mod = 10**9 + 7
# inv = [0, 1]
# for c in range(2, k + 1):
# inv.append((-(mod // c) * inv[mod % c]) % mod)
# s = (((s * (n + 1 - c)) % mod) * inv[c]) % mod
# return s
a = combination(pascal_depth, pascal_k, MOD)
print(a)
| p02862 |
def cmb(n, r, mod):
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 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 = list(map(int, input().split()))
n = (x+y)/3
a = (-x+2*y)/3
#print(n)
#print(a)
if not n.is_integer() or not a.is_integer():
print((0))
else:
n = int(n)
a = int(a)
ans = cmb(n,a,mod)
print(ans)
| def cmb1(n, r, mod):
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 #出力の制限
N = 10**6+10
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 = list(map(int, input().split()))
mod = 10**9+7
if (-x+2*y)>= 0 and (-x+2*y)%3 == 0 and (2*x-y)>= 0 and (2*x-y)%3 == 0:
a = (-x+2*y)//3
b = (2*x-y)//3
print((cmb1(a+b, a, mod)))
else:
print((0))
| p02862 |
MOD=10**9+7
def powmod(a,p):
if p==0:
return 1
elif p==1:
return a
elif p%2==0:
powsq=powmod(a,p//2)
return (powsq**2)%MOD
elif p%2==1:
powsq=powmod(a,p//2)
return (a*powsq**2)%MOD
def invmod(a):
return powmod(a,MOD-2)
X,Y=list(map(int,input().split()))
if (X+Y)%3!=0:
print((0))
else:
u=(2*X-Y)//3
v=(-X+2*Y)//3
if u>=0 and v>=0:
#print(int(u),int(v))
ui=int(u)
vi=int(v)
bunshi=1
for i in range(vi):
bunshi*=ui+vi-i
bunshi%=MOD
bumbo=1
for i in range(vi):
bumbo*=vi-i
bumbo%=MOD
#calculate bunshi/bumbo%MOD as bunshi*bumbo^-1%MOD
print((bunshi*invmod(bumbo)%MOD))
else:
print((0)) | MOD=10**9+7
X,Y=list(map(int,input().split()))
def powmod(a,p):
if p==0:
return 1
elif p==1:
return a
else:
pow2=powmod(a,p//2)
if p%2==0:
return (pow2**2)%MOD
else:
return (a*pow2**2)%MOD
def invmod(a):
return powmod(a,MOD-2)
def comb_mod(n,r):
nPr=1
fact_r=1
for i in range(r):
nPr*=n-i
nPr%=MOD
fact_r*=r-i
fact_r%=MOD
return (nPr*invmod(fact_r))%MOD
if (X+Y)%3!=0:
print((0))
else:
u=(2*X-Y)//3
v=(-X+2*Y)//3
if u>=0 and v>=0:
#print(u,v)
print((comb_mod(u+v,v)))
else:
print((0)) | p02862 |
from functools import reduce
def modpow(a, m):
ret = 1
while m > 0:
if m & 1:
ret = ret * a % mod
a = a * a % mod
m = m >> 1
return ret
def modinv(a):
return modpow(a, mod - 2)
def cmb(n, r):
r = min(r, n - r)
if r == 0:
return 1
over = reduce(lambda a, b: a * b % mod, list(range(n, n - r, -1)))
under = reduce(lambda a, b: a * b % mod, list(range(1, r + 1)))
return over * modinv(under) % mod
x, y = [int(i) for i in input().split()]
if (x + y) % 3 or x > 2 * y or y > 2 * x:
print((0))
else:
mod = 10**9 + 7
print((cmb((x + y) // 3, (2 * x - y) // 3)))
| from functools import reduce
def cmb(n, r):
r = min(r, n - r)
if r == 0:
return 1
over = reduce(lambda a, b: a * b % mod, list(range(n, n - r, -1)))
under = reduce(lambda a, b: a * b % mod, list(range(1, r + 1)))
return over * pow(under, mod-2, mod) % mod
x, y = [int(i) for i in input().split()]
if (x + y) % 3 or x > 2 * y or y > 2 * x:
print((0))
else:
mod = 10**9 + 7
print((cmb((x + y) // 3, (2 * x - y) // 3))) | p02862 |
def bigcmb(N, R, MOD): # nCr(mod p) #n>=10**7,r<=10**6 #前処理不要
if (R < 0) or (N < R):
return 0
R = min(R, N - R)
fact, inv = 1, 1
for i in range(1, R + 1):
fact = (fact * (N - i + 1)) % MOD
inv = (inv * i) % MOD
return fact * pow(inv, MOD - 2, MOD) % MOD
x, y = list(map(int, input().split()))
mod = 10**9+7
if (x + y) % 3 != 0 or x > 2 * y or 2 * x < y:
print((0))
else:
print((bigcmb((x + y) // 3, x - (x + y) // 3, mod)))
| def bigcmb(N, R, MOD): # nCr(mod p) #n>=10**7,r<=10**6 #前処理不要
if (R < 0) or (N < R):
return 0
R = min(R, N - R)
fact, inv = 1, 1
for i in range(1, R + 1):
fact = (fact * (N - i + 1)) % MOD
inv = (inv * i) % MOD
return fact * pow(inv, MOD - 2, MOD) % MOD
x, y = list(map(int, input().split()))
mod = 10 ** 9 + 7
if (x + y) % 3 != 0 or (x > 2 * y) or (2 * x < y):
print((0))
else:
cnt = (x + y) // 3
print((bigcmb(cnt, x - cnt, mod)))
| p02862 |
def bigcmb(N, R, MOD): # nCr(mod p) #n>=10**7,r<=10**6 #前処理不要
if (R < 0) or (N < R):
return 0
R = min(R, N - R)
fact, inv = 1, 1
for i in range(1, R + 1):
fact = (fact * (N - i + 1)) % MOD
inv = (inv * i) % MOD
return fact * pow(inv, MOD - 2, MOD) % MOD
x, y = list(map(int, input().split()))
mod = 10 ** 9 + 7
if (x + y) % 3 != 0 or (x > 2 * y) or (2 * x < y):
print((0))
else:
cnt = (x + y) // 3
print((bigcmb(cnt, x - cnt, mod)))
| def bigcmb(N, R, MOD): # nCr(mod p) #n>=10**7,r<=10**6 #前処理不要
if (R < 0) or (N < R):
return 0
R = min(R, N - R)
fact, inv = 1, 1
for i in range(1, R + 1):
fact = (fact * (N - i + 1)) % MOD
inv = (inv * i) % MOD
return fact * pow(inv, MOD - 2, MOD) % MOD
x, y = list(map(int, input().split()))
mod = 10 ** 9 + 7
if (x + y) % 3 != 0:
print((0))
else:
cnt = (x + y) // 3
print((bigcmb(cnt, x - cnt, mod)))
| p02862 |
MAX_NUM = 10**6 + 1
MOD = 10**9+7
fac = [0 for _ in range(MAX_NUM)]
finv = [0 for _ in range(MAX_NUM)]
inv = [0 for _ in range(MAX_NUM)]
fac[0] = 1
fac[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2,MAX_NUM):
fac[i] = fac[i-1] * i % MOD
inv[i] = MOD - inv[MOD%i] * (MOD // i) % MOD
finv[i] = finv[i-1] * inv[i] % MOD
def combinations(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
X,Y = list(map(int,input().split()))
if (-Y + 2*X) % 3 == 0 and (2*Y - X) %3 == 0:
x = (-Y + 2*X) // 3
y = (2*Y - X) // 3
result = combinations(x+y,min(x,y))
print((int(result % MOD)))
else:
print((0))
| MAX_NUM = 10**6 + 1
MOD = 10**9+7
fac = [0 for _ in range(MAX_NUM)]
finv = [0 for _ in range(MAX_NUM)]
inv = [0 for _ in range(MAX_NUM)]
fac[0] = 1
fac[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2,MAX_NUM):
fac[i] = fac[i-1] * i % MOD
inv[i] = MOD - inv[MOD%i] * (MOD // i) % MOD
finv[i] = finv[i-1] * inv[i] % MOD
def combinations(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
X,Y = list(map(int,input().split()))
if (-Y + 2*X) % 3 != 0 or (2*Y - X) %3 != 0 or (-Y + 2*X) < 0 or (2*Y - X) <0:
print((0))
else:
x = (-Y + 2*X) // 3
y = (2*Y - X) // 3
result = combinations(x+y,min(x,y))
print((int(result % MOD)))
| p02862 |
#ABC145D
MOD = 10 ** 9 + 7
import math
x,y = list(map(int,input().split()))
a,b = -1,-1
for i in range(x+1):
m = 0
if (x-i) % 2 == 0:
m = (x-i) // 2
if 2*i + m == y:
if i >= 0 and m >= 0:
a = i
b = m
break
else:
continue
MAX_N = 10**6
fact = [1]
fact_inv = [0]*(MAX_N+4)
for i in range(MAX_N+3):
fact.append(fact[-1]*(i+1)%MOD)
fact_inv[-1] = pow(fact[-1],MOD-2,MOD)
for i in range(MAX_N+2,-1,-1):
fact_inv[i] = fact_inv[i+1]*(i+1)%MOD
def com(n,k,mod):
return fact[n] * fact_inv[k] % mod * fact_inv[n-k] %mod
if a == -1 and b == -1:
print((0))
else:
print((com(a+b,a,MOD))) | #ABC145D
MOD = 10 ** 9 + 7
import math
x,y = list(map(int,input().split()))
a,b = -1,-1
for i in range(x+1):
m = 0
if (x-i) % 2 == 0:
m = (x-i) // 2
if 2*i + m == y:
if i >= 0 and m >= 0:
a = i
b = m
break
else:
continue
def kai(x):
an = 1
for i in range(1,x+1):
an = an * i % MOD
return an
def pow_k(x, n):
if n == 0:
return 1
K = 1
while n > 1:
if n % 2 != 0:
K = K * x % MOD
x = x ** 2 % MOD
n //= 2
return K * x % MOD
al = kai(a)
be = kai(b)
if a == -1 and b == -1:
print((0))
else:
print((( kai(a+b) * pow_k(al,MOD-2)) % MOD * pow_k(be,MOD-2) % MOD )) | p02862 |
import sys
from math import factorial
def cmb(n, r, mod):
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
x, y = list(map(int, sys.stdin.readline().split()))
if (x + y)%3 != 0:
print((0))
sys.exit()
if y < x/2 and y > 2*x:
print((0))
sys.exit()
count = 0
while(True):
if y == 1/2*x:
break
else:
x -= 1
y -= 2
count += 1
sum = count + y
mod = 10**9+7 #出力の制限
N = 10**4
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
for i in range( 2, sum + 1 ):
g1.append( ( g1[-1] * i ) % mod )
inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
g2.append( (g2[-1] * inverse[-1]) % mod )
if count < y:
a = cmb(sum,count,mod)
else:
a = cmb(sum, y, mod)
print(a)
| import sys
from math import factorial
def cmb(n, r, mod):
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
x, y = list(map(int, sys.stdin.readline().split()))
if (x + y)%3 != 0:
print((0))
sys.exit()
if y < x/2 and y > 2*x:
print((0))
sys.exit()
count1 = int((y-2*x)/(-3))
count2 = int((x-2*y)/(-3))
sum = count1 + count2
N = 10**4
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
for i in range( 2, sum + 1 ):
g1.append( ( g1[-1] * i ) % mod )
inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
g2.append( (g2[-1] * inverse[-1]) % mod )
a = cmb(sum,count1,mod)
print(a)
| p02862 |
# 2019-11-16 21:01:15(JST)
import sys
# import collections
# import math
# from string import ascii_lowercase, ascii_uppercase, digits
# from bisect import bisect_left as bi_l, bisect_right as bi_r
# import itertools
# from functools import reduce
# import operator as op
# from scipy.misc import comb # float
# import numpy as np
def comb(n, r, mod):
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 #出力の制限
N = 10**6 # 問題によってNの大きさは変える
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 )
def main():
x, y = [int(x) for x in sys.stdin.readline().split()]
# n(+1, +2), m(+2, +1)
n, m = (2 * y - x) / 3, (2 * x - y) / 3
if n != abs(int(n)) or m != abs(int(m)):
print((0))
sys.exit()
else:
n, m = int(n), int(m)
ans = comb(n+m, m, mod)
print(ans)
if __name__ == "__main__":
main()
| # 2019-11-16 21:01:15(JST)
import sys
# import collections
# import math
# from string import ascii_lowercase, ascii_uppercase, digits
# from bisect import bisect_left as bi_l, bisect_right as bi_r
# import itertools
# from functools import reduce
# import operator as op
# from scipy.misc import comb # float
# import numpy as np
mod = 10 ** 9 + 7
def comb(n, r):
r = min(r, n - r)
if r == 0: return 1
if r == 1: return n
numerator = list(range(n-r+1, n+1))
denominator = list(range(1, r+1))
for p in range(2,r+1):
pivot = denominator[p - 1]
if pivot > 1:
offset = (n - r) % p
for k in range(p-1,r,p):
numerator[k - offset] /= pivot
denominator[k] /= pivot
result = 1
for k in range(r):
if numerator[k] > 1:
result *= int(numerator[k])
return result
def main():
x, y = [int(x) for x in sys.stdin.readline().split()]
# n(+1, +2), m(+2, +1)
n, m = (2 * y - x) / 3, (2 * x - y) / 3
if n != abs(int(n)) or m != abs(int(m)):
print((0))
sys.exit()
else:
n, m = int(n), int(m)
ans = comb(n+m, n) % mod
print(ans)
if __name__ == "__main__":
main()
| p02862 |
X, Y = list(map(int, input().split()))
def mod_Combination(n, k, mod):
def ext_gcd(a, b):
if b == 0:
return a, 1, 0
else:
d,x,y = ext_gcd(b,a%b)
x-=(a//b)*y
return d,y,x
p,q=1,1
for i in range(n-k+1, n+1):
p=(p*i)%mod
for i in range(2, k+1):
q=(q*i)%mod
return int(p*(ext_gcd(q, mod)[1]%mod)%mod)
if X > Y:
X, Y = Y, X
a = (2*X - Y)/3
b = (2*Y - X)/3
if (X+Y)%3 != 0:
ans = 0
elif a<0 or b<0:
ans = 0
else:
ans = mod_Combination(int(a + b), int(a), 10**9 + 7)
print(ans)
| X, Y = list(map(int, input().split()))
def mod_Combination(n, k, mod):
def ext_gcd(a, b):
if b == 0:
return a, 1, 0
else:
d,x,y = ext_gcd(b,a%b)
x-=(a//b)*y
return d,y,x
p,q=1,1
for i in range(n-k+1, n+1):
p=(p*i)%mod
for i in range(2, k+1):
q=(q*i)%mod
return int(p*(ext_gcd(q, mod)[1]%mod)%mod)
a = (2*X - Y)/3
b = (2*Y - X)/3
if (X+Y)%3 != 0:
ans = 0
elif a<0 or b<0:
ans = 0
else:
ans = mod_Combination(int(a + b), int(a), 10**9 + 7)
print(ans)
| p02862 |
# nCk(mod p)の計算
from math import factorial
X, Y = list(map(int, input().split()))
MOD = 10**9+7
MAX = 10**6+1
# a!のテーブルfact
fact = [0] * MAX
# (a!)^-1のテーブルfinv
finv = [0] * MAX
def comb_init():
# a!と(a!)^-1のテーブルを作る
# 累積積のイメージ
fact[0] = fact[1] = 1
finv[0] = finv[1] = 1
for i in range(2, MAX):
fact[i] = i * fact[i-1] % MOD
finv[i] = pow(i, -1, MOD) * finv[i-1] % MOD
def comb(n, r):
return fact[n] * (finv[n-r] * finv[r] % MOD) % MOD
if (X+Y) % 3 != 0:
print((0))
else:
num = (X+Y)//3
p = (Y - X + num) // 2
q = (X + num - Y) // 2
if not num >= min(p, q) >= 0:
print((0))
exit()
comb_init()
print((comb(num, min(p, q)))) | X, Y = list(map(int, input().split()))
MOD = 10**9+7
MAX = 10**6+1
# a!のテーブルfact
fact = [0] * MAX
def comb_init():
# 累積積のイメージ
fact[0] = fact[1] = 1
for i in range(2, MAX):
fact[i] = i * fact[i-1] % MOD
def comb(n, r):
return fact[n]*pow(fact[r], -1, MOD)*pow(fact[n-r], -1, MOD)%MOD
if (X+Y) % 3 != 0:
print((0))
else:
num = (X+Y)//3
p = (Y - X + num) // 2
q = (X + num - Y) // 2
if not num >= min(p, q) >= 0:
print((0))
exit()
comb_init()
print((comb(num, min(p, q)))) | p02862 |
mod = 10 ** 9 + 7
x, y = list(map(int, input().split()))
a = (2 * y - x) // 3
b = (2 * x - y) // 3
if (x + y) % 3 != 0 or a < 0 or b < 0:
print((0))
exit()
n = a + b
r = min(a, b)
ans = 1
for i in range(r):
ans = ans * (n - i) * pow(i + 1, mod - 2, mod) % mod
print(ans)
| def factorial(n, r, p):
ret = 1
for i in range(n, n - r, -1):
ret = (ret * i) % p
return ret
def comb(n, r, p):
r = min(r, n - r)
return (factorial(n, r, p) * pow(factorial(r, r, p), p - 2, p)) % p
mod = 10 ** 9 + 7
x, y = list(map(int, input().split()))
a = (2 * y - x) // 3
b = (2 * x - y) // 3
if (x + y) % 3 != 0 or a < 0 or b < 0:
ans = 0
else:
ans = comb(a + b, a, mod)
print(ans)
| p02862 |
def cmb(n, r, mod):
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 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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=list(map(int,input().split()))
if (X+Y)%3!=0:
print((0))
exit()
n=(X+Y)//3
k=Y-(X+Y)//3
if k<0 or k>n:
print((0))
exit()
#print("n,k:",n,k)
print((cmb(n,k,mod))) | X, Y = list(map(int, input().split()))
MOD = 10 ** 9 + 7
if (X + Y) % 3 != 0:
print((0))
exit()
if abs(X - Y) > (X + Y) // 3:
print((0))
exit()
n = (X + Y) // 3 + 1
k = ((X - Y) + n + 1) // 2
SIZE = max(n, k)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
def comb(n, r, mod):
if r < 0 or r > n:
return 0
r = min(r, n - r)
return g1[n] * g2[r] * g2[n - r] % mod
for i in range(2, SIZE):
g1.append((g1[-1] * i) % MOD)
inverse.append((-inverse[MOD % i] * (MOD // i) ) % MOD)
g2.append((g2[-1] * inverse[-1]) % MOD)
print((comb(n - 1, k - 1, MOD))) | p02862 |
# -*- coding: utf-8 -*-
import sys
import math
import os
import itertools
import string
import heapq
import _collections
from collections import Counter
from collections import defaultdict
from functools import lru_cache
import bisect
import re
import queue
class Scanner():
@staticmethod
def int():
return int(sys.stdin.readline().rstrip())
@staticmethod
def string():
return sys.stdin.readline().rstrip()
@staticmethod
def map_int():
return [int(x) for x in Scanner.string().split()]
@staticmethod
def string_list(n):
return [eval(input()) for i in range(n)]
@staticmethod
def int_list_list(n):
return [Scanner.map_int() for i in range(n)]
@staticmethod
def int_cols_list(n):
return [int(eval(input())) for i in range(n)]
class Math():
@staticmethod
def gcd(a, b):
if b == 0:
return a
return Math.gcd(b, a % b)
@staticmethod
def lcm(a, b):
return (a * b) // Math.gcd(a, b)
@staticmethod
def roundUp(a, b):
return -(-a // b)
@staticmethod
def toUpperMultiple(a, x):
return Math.roundUp(a, x) * x
@staticmethod
def toLowerMultiple(a, x):
return (a // x) * x
@staticmethod
def nearPow2(n):
if n <= 0:
return 0
if n & (n - 1) == 0:
return n
ret = 1
while(n > 0):
ret <<= 1
n >>= 1
return ret
@staticmethod
def sign(n):
if n == 0:
return 0
if n < 0:
return -1
return 1
@staticmethod
def isPrime(n):
if n < 2:
return False
if n == 2:
return True
if n % 2 == 0:
return False
d = int(n ** 0.5) + 1
for i in range(3, d + 1, 2):
if n % i == 0:
return False
return True
class PriorityQueue:
def __init__(self, l=[]):
self.__q = l
heapq.heapify(self.__q)
return
def push(self, n):
heapq.heappush(self.__q, n)
return
def pop(self):
return heapq.heappop(self.__q)
sys.setrecursionlimit(1000000)
MOD = int(1e09) + 7
INF = int(1e15)
def main():
# sys.stdin = open("sample.txt")
X, Y = Scanner.map_int()
if (X + Y) % 3 != 0:
print((0))
return
n = (X + Y) // 3
X -= n
Y -= n
MAX = 670000
fac = [0 for _ in range(MAX)]
finv = [0 for _ in range(MAX)]
inv = [0 for _ in range(MAX)]
fac[0] = fac[1] = 1
finv[0] = 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
N = X + Y
if N < X:
print((0))
return
if N < 0 or X < 0:
print((0))
return
ans = fac[N] * (finv[X] * finv[Y] % MOD) % MOD
print(ans)
return
if __name__ == "__main__":
main()
| # -*- coding: utf-8 -*-
import sys
import math
import os
import itertools
import string
import heapq
import _collections
from collections import Counter
from collections import defaultdict
from collections import deque
from functools import lru_cache
import bisect
import re
import queue
import decimal
class Scanner():
@staticmethod
def int():
return int(sys.stdin.readline().rstrip())
@staticmethod
def string():
return sys.stdin.readline().rstrip()
@staticmethod
def map_int():
return [int(x) for x in Scanner.string().split()]
@staticmethod
def string_list(n):
return [Scanner.string() for i in range(n)]
@staticmethod
def int_list_list(n):
return [Scanner.map_int() for i in range(n)]
@staticmethod
def int_cols_list(n):
return [Scanner.int() for i in range(n)]
class Math():
@staticmethod
def gcd(a, b):
if b == 0:
return a
return Math.gcd(b, a % b)
@staticmethod
def lcm(a, b):
return (a * b) // Math.gcd(a, b)
@staticmethod
def divisor(n):
res = []
i = 1
for i in range(1, int(n ** 0.5) + 1):
if n % i == 0:
res.append(i)
if i != n // i:
res.append(n // i)
return res
@staticmethod
def round_up(a, b):
return -(-a // b)
@staticmethod
def is_prime(n):
if n < 2:
return False
if n == 2:
return True
if n % 2 == 0:
return False
d = int(n ** 0.5) + 1
for i in range(3, d + 1, 2):
if n % i == 0:
return False
return True
@staticmethod
def fact(N):
res = {}
tmp = N
for i in range(2, int(N ** 0.5 + 1) + 1):
cnt = 0
while tmp % i == 0:
cnt += 1
tmp //= i
if cnt > 0:
res[i] = cnt
if tmp != 1:
res[tmp] = 1
if res == {}:
res[N] = 1
return res
def pop_count(x):
x = x - ((x >> 1) & 0x5555555555555555)
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f
x = x + (x >> 8)
x = x + (x >> 16)
x = x + (x >> 32)
return x & 0x0000007f
MOD = int(1e09) + 7
INF = int(1e15)
def modinv(a):
b = MOD
u = 1
v = 0
while b:
t = a // b
a -= t * b
a, b = b, a
u -= t * v
u, v = v, u
u %= MOD
if u < 0:
u += MOD
return u
def factorial(N):
if N == 0 or N == 1:
return 1
res = N
for i in range(N - 1, 1, -1):
res *= i
res %= MOD
return res
def solve():
X, Y = Scanner.map_int()
if (X + Y) % 3 != 0:
print((0))
return
B = (2 * Y - X) // 3
A = (2 * X - Y) // 3
if A < 0 or B < 0:
print((0))
return
n = factorial(A + B)
m = factorial(A)
l = factorial(B)
ans = n * modinv(m * l % MOD) % MOD
print(ans)
def main():
# sys.setrecursionlimit(1000000)
# sys.stdin = open("sample.txt")
# T = Scanner.int()
# for _ in range(T):
# solve()
# print('YNeos'[not solve()::2])
solve()
if __name__ == "__main__":
main()
| p02862 |
def main():
X, Y = (int(i) for i in input().split())
fac = [0] * max(X, Y)
finv = [0] * max(X, Y)
inv = [0] * max(X, Y)
MOD = (10**9) + 7
def COMinit(m):
fac[0] = 1
finv[0] = 1
if m > 1:
fac[1] = 1
finv[1] = 1
inv[1] = 1
for i in range(2, m):
fac[i] = fac[i-1] * i % MOD
inv[i] = MOD - inv[MOD % i] * (MOD // i) % MOD
finv[i] = finv[i - 1] * inv[i] % MOD
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
COMinit(max(X, Y))
if (X+Y) % 3 != 0:
return print(0)
n = (2*Y - X) // 3
m = (2*X - Y) // 3
print(COM(n+m, m))
if __name__ == '__main__':
main()
| def main():
X, Y = (int(i) for i in input().split())
if (X+Y) % 3 != 0:
return print(0)
m = (X + Y)//3 + 3
fac = [0] * m
finv = [0] * m
inv = [0] * m
MOD = 10**9 + 7
def COMBinitialize(m):
fac[0] = 1
finv[0] = 1
if m > 1:
fac[1] = 1
finv[1] = 1
inv[1] = 1
for i in range(2, m):
fac[i] = fac[i-1] * i % MOD
inv[i] = MOD - inv[MOD % i] * (MOD // i) % MOD
finv[i] = finv[i - 1] * inv[i] % MOD
def COMB(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
COMBinitialize(m)
n = (X+Y)//3
k = X - n
print(COMB(n, k))
if __name__ == '__main__':
main()
| p02862 |
import math
def cmb(n, r, mod):
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 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 = list(map(int,input().split()))
sum = 0
if x%2 == 1:
for k in range((x+1)//2):
k = 2*k +1
l = (x-k)//2
if l+2*k == y:
sum += cmb(k+l,l,mod)
sum = sum%mod
print(sum)
if x%2 == 0:
for k in range(x//2):
k = 2*k
l = (x-k)//2
if l+2*k == y:
sum += cmb(k+l,l,mod)
sum = sum%mod
print(sum) | def cmb(n,r,mod):
bunshi=1
bunbo=1
for i in range(r):
bunbo = bunbo*(i+1)%mod
bunshi = bunshi*(n-i)%mod
return (bunshi*pow(bunbo,mod-2,mod))%mod
mod = 10**9+7
x,y = list(map(int,input().split()))
sum = 0
if x%2 == 1:
for k in range((x+1)//2):
k = 2*k +1
l = (x-k)//2
if l+2*k == y:
sum += cmb(k+l,l,mod)
sum = sum%mod
print(sum)
if x%2 == 0:
for k in range(x//2):
k = 2*k
l = (x-k)//2
if l+2*k == y:
sum += cmb(k+l,l,mod)
sum = sum%mod
print(sum) | p02862 |
from math import factorial
def com(n,k,mod,fac,infac):
k=min(k,n-k)
return fac[n]*infac[k]*infac[n-k]%mod
def cominit(mod,n):
fac=[1,1]
infac=[1,1]
inv=[0,1]
for i in range(2,n+1):
fac.append(fac[-1]*i%mod)
inv.append(-inv[mod%i]*(mod//i)%mod)
infac.append(infac[-1]*inv[-1]%mod)
return fac,infac
def main():
x,y=list(map(int,input().split()))
if (x+y)%3!=0:
print((0))
return
temp=int((x+y)/3)
if temp*2 < x or temp > x:
print((0))
return
f,inf=cominit(10**9+7,temp)
# n,kはしっかりはっきりさせよ明日
# ans=factorial(temp) / factorial(x-temp) / factorial(2*temp-x)
ans=com(temp,abs(x-temp),10**9+7,f,inf)
print(ans)
if __name__ == '__main__':
main()
| # nCkの計算するやつ
# (n!)/(k!(n-k)!) mod p
# (n!) * (k!)^-1 * ((n-k)!)^-1 mod p
def comInit(MOD, n):
fact=[1,1] # fact[n]はnの階乗
invr=[0,1] # invr[n]はnの逆元
invr_fact=[1,1] # invr_fact[n]は逆元の階乗
for i in range(2,n+1):
fact.append(fact[-1]*i%MOD)
invr.append(-invr[MOD%i]*(MOD//i)%MOD)
invr_fact.append(invr_fact[-1]*invr[-1]%MOD)
return fact,invr_fact
def calCom(n,k,MOD,fact,invr_fact):
k=min(k,n-k)
return fact[n]*invr_fact[k]*invr_fact[n-k]%MOD
def main():
x,y=list(map(int,input().split()))
if (x+y)%3!=0:
print((0))
return
temp=int((x+y)/3)
if temp*2 < x or temp > x:
print((0))
return
f,inf=comInit(10**9+7,temp)
# n,kはしっかりはっきりさせよ明日
# ans=factorial(temp) / factorial(x-temp) / factorial(2*temp-x)
ans=calCom(temp,abs(x-temp),10**9+7,f,inf)
print(ans)
if __name__ == '__main__':
main()
| p02862 |
from sys import exit
def mpow(x, n):
result = 1
while n != 0:
if n & 1 == 1:
result *= x
result %= 1000000007
x *= x
x %= 1000000007
n >>= 1
return result
p = 1000000007
X, Y = list(map(int, input().split()))
if (X+Y) % 3 != 0:
print((0))
exit()
a = (2 * Y - X) // 3
b = (2 * X - Y) // 3
if a < 0 or b < 0:
print((0))
exit()
n = a + b
k = min(a, b)
if n == 0 and k == 0:
print((1))
exit()
if n < k or k < 0:
print((0))
exit()
fac = [0] * (n + 1)
fac[0] = 1
for i in range(n):
fac[i + 1] = fac[i] * (i + 1) % p
print((fac[n] * mpow(fac[n - k], p - 2) * mpow(fac[k], p - 2) % p))
| from sys import exit
def mpow(x, n):
result = 1
while n != 0:
if n & 1 == 1:
result *= x
result %= 1000000007
x *= x
x %= 1000000007
n >>= 1
return result
def mcomb(n, k):
if n == 0 and k == 0:
return 1
if n < k or k < 0:
return 0
fac = [0] * (n + 1)
fac[0] = 1
for i in range(n):
fac[i + 1] = fac[i] * (i + 1) % p
return fac[n] * mpow(fac[n - k], p - 2) * mpow(fac[k], p - 2) % p
p = 1000000007
X, Y = list(map(int, input().split()))
if (X+Y) % 3 != 0:
print((0))
exit()
a = (2 * Y - X) // 3
b = (2 * X - Y) // 3
if a < 0 or b < 0:
print((0))
exit()
print((mcomb(a + b, min(a, b))))
| p02862 |
# フェルマーの小定理
X, Y = list(map(int, input().split()))
m = 1000000007
if (X + Y) % 3 != 0:
print((0))
exit()
a = (2 * Y - X) // 3
b = (2 * X - Y) // 3
if a < 0 or b < 0:
print((0))
exit()
n = a + b
fac = [0] * (n + 1)
fac[0] = 1
for i in range(n):
fac[i + 1] = fac[i] * (i + 1) % m
def mcomb(n, k):
if n == 0 and k == 0:
return 1
if n < k or k < 0:
return 0
return fac[n] * pow(fac[n - k], m - 2, m) * pow(fac[k], m - 2, m) % m
print((mcomb(n, a)))
| # フェルマーの小定理
X, Y = list(map(int, input().split()))
m = 1000000007
def make_factorial_table(n):
result = [0] * (n + 1)
result[0] = 1
for i in range(1, n + 1):
result[i] = result[i - 1] * i % m
return result
def mcomb(n, k):
if n == 0 and k == 0:
return 1
if n < k or k < 0:
return 0
return fac[n] * pow(fac[n - k], m - 2, m) * pow(fac[k], m - 2, m) % m
if (X + Y) % 3 != 0:
print((0))
exit()
a = (2 * Y - X) // 3
b = (2 * X - Y) // 3
if a < 0 or b < 0:
print((0))
exit()
n = a + b
fac = make_factorial_table(n)
print((mcomb(n, a)))
| p02862 |
# フェルマーの小定理
X, Y = list(map(int, input().split()))
m = 1000000007
def make_factorial_table(n):
result = [0] * (n + 1)
result[0] = 1
for i in range(1, n + 1):
result[i] = result[i - 1] * i % m
return result
def mcomb(n, k):
if n == 0 and k == 0:
return 1
if n < k or k < 0:
return 0
return fac[n] * pow(fac[n - k], m - 2, m) * pow(fac[k], m - 2, m) % m
if (X + Y) % 3 != 0:
print((0))
exit()
a = (2 * Y - X) // 3
b = (2 * X - Y) // 3
if a < 0 or b < 0:
print((0))
exit()
n = a + b
fac = make_factorial_table(n)
print((mcomb(n, a)))
| # フェルマーの小定理
X, Y = list(map(int, input().split()))
m = 1000000007
def mcomb(n, k):
a = 1
b = 1
for i in range(k):
a *= n - i
a %= m
b *= i + 1
b %= m
return a * pow(b, m - 2, m) % m
if (X + Y) % 3 != 0:
print((0))
exit()
a = (2 * Y - X) // 3
b = (2 * X - Y) // 3
if a < 0 or b < 0:
print((0))
exit()
n = a + b
print((mcomb(n, a)))
| p02862 |
import math
P = 10**9 + 7
X, Y = list(map(int, input().split()))
if (X + Y) % 3 > 0:
print((0))
exit()
n = (X + Y) // 3
x = X - n
y = Y - n
if 0 > x or 0 > y:
print((0))
exit()
fact = [0] * (x + y + 1)
inv = [0] * (x + y + 1)
fact_inv = [0] * (x + y + 1)
fact[0], fact[1] = 1, 1
inv[0], inv[1] = 0, 1
fact_inv[0], fact_inv[1] = 1, 1
for i in range(2, x + y + 1):
fact[i] = (fact[i - 1] * i) % P
inv[i] = (-inv[P % i] * (P // i)) % P
fact_inv[i] = (fact_inv[i - 1] * inv[i]) % P
print(((fact[x + y] * fact_inv[x] * fact_inv[y]) % P))
| P = 10**9 + 7
X, Y = list(map(int, input().split()))
if (X + Y) % 3 > 0:
print((0))
exit()
n = (X + Y) // 3
x = X - n
y = Y - n
if 0 > x or 0 > y:
print((0))
exit()
fact = [0] * (x + y + 1)
inv = [0] * (x + y + 1)
fact_inv = [0] * (x + y + 1)
fact[0], fact[1] = 1, 1
inv[0], inv[1] = 0, 1
fact_inv[0], fact_inv[1] = 1, 1
for i in range(2, x + y + 1):
fact[i] = (fact[i - 1] * i) % P
print(((fact[x + y] * pow(fact[x], P - 2, P) * pow(fact[y], P - 2, P)) % P))
| p02862 |
P = 10**9 + 7
X, Y = list(map(int, input().split()))
if (X + Y) % 3 > 0:
print((0))
exit()
n = (X + Y) // 3
x = X - n
y = Y - n
if 0 > x or 0 > y:
print((0))
exit()
fact = [0] * (x + y + 1)
inv = [0] * (x + y + 1)
fact_inv = [0] * (x + y + 1)
fact[0], fact[1] = 1, 1
inv[0], inv[1] = 0, 1
fact_inv[0], fact_inv[1] = 1, 1
for i in range(2, x + y + 1):
fact[i] = (fact[i - 1] * i) % P
print(((fact[x + y] * pow(fact[x], P - 2, P) * pow(fact[y], P - 2, P)) % P))
| def fact(n, k, mod):
res = 1
for i in range(k):
res = res * (n - i) % mod
return res
def c(x, y, mod):
y = min(x, x - y)
return (fact(x, y, mod) * pow(fact(y, y, mod), mod - 2 , mod)) % mod
P = 10**9 + 7
X, Y = list(map(int, input().split()))
if (X + Y) % 3 > 0:
print((0))
exit()
n = (X + Y) // 3
x = X - n
y = Y - n
if 0 > x or 0 > y:
print((0))
exit()
print((c(x + y, x, P))) | p02862 |
# https://atcoder.jp/contests/abc145/tasks/abc145_d
class Combination: # 計算量は O(n_max + log(mod))
def __init__(self, n_max, mod=10**9+7):
self.mod = mod
f = 1
self.fac = fac = [f]
for i in range(1, n_max+1): # 階乗(= n_max !)の逆元を生成
f = f * i % mod # 動的計画法による階乗の高速計算
fac.append(f) # fac は階乗のリスト
f = pow(f, mod-2, mod) # 階乗から階乗の逆元を計算。フェルマーの小定理より、 a^-1 = a^(p-2) (mod p) if p = prime number and p and a are coprime
# python の pow 関数は自動的に mod の下での高速累乗を行ってくれる
self.facinv = facinv = [f]
for i in range(n_max, 0, -1): # 上記の階乗の逆元から階乗の逆元のリストを生成（＝ facinv ）
f = f * i % mod
facinv.append(f)
facinv.reverse()
# "n 要素" は区別できる n 要素
# "k グループ" はちょうど k グループ
def __call__(self, n, r): # self.C と同じ
return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod
def C(self, n, r):
if not 0 <= r <= n: return 0
return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod
X, Y = list(map(int, input().split()))
if (2*Y- X) % 3 or (2*X- Y) % 3:
print((0))
exit()
x = (2*Y - X) // 3
y = (2*X - Y) // 3
n = x + y
r = x
mod = 10**9 + 7
f = 1
for i in range(1, n + 1):
f = f*i % mod
fac = f
f = pow(f, mod-2, mod)
facinv = [f]
for i in range(n, 0, -1):
f = f*i % mod
facinv.append(f)
facinv.append(1)
comb = Combination(n)
print((comb.C(n,r))) | # https://atcoder.jp/contests/abc145/tasks/abc145_d
X, Y = list(map(int, input().split()))
if (2*Y- X) % 3 or (2*X- Y) % 3:
print((0))
exit()
x = (2*Y - X) // 3
y = (2*X - Y) // 3
if x < 0 or y < 0:
print((0))
exit()
n = x + y
r = x
mod = 10**9 + 7
f = 1
for i in range(1, n + 1):
f = f*i % mod
fac = f
f = pow(f, mod-2, mod)
facinv = [f]
for i in range(n, 0, -1):
f = f*i % mod
facinv.append(f)
facinv.append(1)
print((fac * facinv[r] * facinv[n - r] % mod)) | p02862 |
# https://atcoder.jp/contests/abc145/tasks/abc145_d
X, Y = list(map(int, input().split()))
if (2*Y- X) % 3 or (2*X- Y) % 3:
print((0))
exit()
x = (2*Y - X) // 3
y = (2*X - Y) // 3
if x < 0 or y < 0:
print((0))
exit()
n = x + y
r = x
mod = 10**9 + 7
f = 1
for i in range(1, n + 1):
f = f*i % mod
fac = f
f = pow(f, mod-2, mod)
facinv = [f]
for i in range(n, 0, -1):
f = f*i % mod
facinv.append(f)
facinv.append(1)
print((fac * facinv[r] * facinv[n - r] % mod)) | from functools import reduce
def combination2(n, r, MOD=10**9+7):
if not 0 <= r <= n: return 0
r = min(r, n - r)
numerator = reduce(lambda x, y: x * y % MOD, list(range(n, n - r, -1)), 1)
denominator = reduce(lambda x, y: x * y % MOD, list(range(1, r + 1)), 1)
return numerator * pow(denominator, MOD - 2, MOD) % MOD
X, Y = list(map(int, input().split()))
if (2*X-Y)%3 or (2*Y-X)%3:
print((0))
exit()
x, y = (2*X-Y)//3, (2*Y-X)//3
print((combination2(x+y,x)))
| p02862 |
import sys
import math
def cmb(n, r):
if n - r < r: r = n - r
if r == 0: return 1
if r == 1: return n
numerator = [n - r + k + 1 for k in range(r)]
denominator = [k + 1 for k in range(r)]
for p in range(2,r+1):
pivot = denominator[p - 1]
if pivot > 1:
offset = (n - r) % p
for k in range(p-1,r,p):
numerator[k - offset] /= pivot
denominator[k] /= pivot
result = 1
for k in range(r):
if numerator[k] > 1:
result *= int(numerator[k])
return result
a,b=list(map(int,input().split()))
c=int((2*a-b)/3)
if (a+b)%3!=0:
print('0')
sys.exit()
if c<0 or (a+b)//3<c:
print('0')
sys.exit()
print((cmb((a+b)//3,c)%1000000007)) | x,y=list(map(int,input().split()))
def cmb(n, r):
if n - r < r: r = n - r
if r == 0: return 1
if r == 1: return n
numerator = [n - r + k + 1 for k in range(r)]
denominator = [k + 1 for k in range(r)]
for p in range(2,r+1):
pivot = denominator[p - 1]
if pivot > 1:
offset = (n - r) % p
for k in range(p-1,r,p):
numerator[k - offset] /= pivot
denominator[k] /= pivot
result = 1
for k in range(r):
if numerator[k] > 1:
result *= int(numerator[k])
return result
if x/y>2 or x/y<0.5 or (x+y)%3!=0:
print((0))
exit()
a=(2*x-y)//3
print((cmb((x+y)//3,a)%(10**9+7))) | p02862 |
def cmb(n, r, mod):
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 # 出力の制限
N = 10 ** 6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
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 = list(map(int, input().split()))
if (x+y) % 3 != 0:
print((0))
exit()
count = (x+y)//3
x -= count
y -= count
ans = cmb(x+y, min(x, y), mod)
print(ans) | def nCr(n,r,mod = 10**9+7):
r = min(n-r,r)
numer = denom = 1
for i in range(1,r+1):
numer = numer * (n+1-i) %mod
denom = denom * i % mod
return numer * pow(denom,mod-2,mod) %mod
x, y = list(map(int, input().split()))
if (x+y) % 3 != 0:
print((0))
exit()
count = (x+y)//3
x -= count
y -= count
if x<0 or y<0:
print((0))
exit()
ans = nCr(x+y, x)
print(ans)
| p02862 |
#lにa回、rにb回進む
x,y = list(map(int,input().split()))
#x = a +2b
#y = 2a+b
#x+y = 3a+3b
#a+b = (x+y)/3
#b=x-a+b
b = x-(x+y)/3
a = (x-2*b)
ans = 0
#print("a:{} b:{}".format(a,b))
if a<0 or b<0 or b-int(b)>0.00001 or a-int(a)>0.00001:
print(ans)
exit()
MAX = 1000000;
MOD = 1000000007;
fac = [0 for i in range(MAX)]
finv = [0 for i in range(MAX)]
inv = [0 for i in range(MAX)]
#テーブルを作る前処理
def COMinit():
fac[0],fac[1] = 1,1
finv[0],finv[1] = 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
#二項係数計算
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
COMinit()
print((COM(int(a+b),int(a)))) | #lにa回、rにb回進む
x,y = list(map(int,input().split()))
#x = a +2b
#y = 2a+b
#x+y = 3a+3b
#a+b = (x+y)/3
#b=x-a+b
b = x-(x+y)/3
a = (x-2*b)
ans = 0
#print("a:{} b:{}".format(a,b))
if a<0 or b<0 or b-int(b)>0.00001 or a-int(a)>0.00001:
print(ans)
exit()
MAX = int(a+b)+1
MOD = 1000000007
fac = [0 for i in range(MAX)]
finv = [0 for i in range(MAX)]
inv = [0 for i in range(MAX)]
#テーブルを作る前処理
def COMinit():
fac[0],fac[1] = 1,1
finv[0],finv[1] = 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
#二項係数計算
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
COMinit()
print((COM(int(a+b),int(a)))) | p02862 |
from sys import stdin, setrecursionlimit
def initialize_cmb(m, mod=10 ** 9 + 7):
fac = [1]
finv = [1]
inv = [0] * (m + 1)
if m >= 1:
fac.append(1)
finv.append(1)
inv[1] = 1
pre_fac = 1
pre_finv = 1
for i in range(2, m + 1):
pre_fac = pre_fac * i % mod
fac.append(pre_fac)
inv[i] = mod - inv[mod % i] * (mod // i) % mod
pre_finv = pre_finv * inv[i] % mod
finv.append(pre_finv)
return fac, finv
def cmb(n, k, fac, finv, mod=10 ** 9 + 7):
if n < k:
return 0
if n < 0 or k < 0:
return 0
return fac[n] * (finv[k] * finv[n - k] % mod) % mod
def main():
mod = 10 ** 9 + 7
input = stdin.buffer.readline
x, y = list(map(int, input().split()))
if (x + y) % 3 != 0 or 2 * x < y or 2 * y < x:
print((0))
else:
fac, finv = initialize_cmb((x + y) // 3, mod)
x_min = (x + y) // 3
print((cmb((x + y) // 3, x - x_min, fac, finv, mod)))
if __name__ == "__main__":
setrecursionlimit(10000)
main()
| from sys import stdin, setrecursionlimit
def cmb(n, r, mod=10 ** 9 + 7):
r = min(r, n - r)
x = y = 1
for i in range(r):
x *= n - i
x %= mod
y *= i + 1
y %= mod
return x * pow(y, mod - 2, mod) % mod
def main():
mod = 10 ** 9 + 7
input = stdin.buffer.readline
x, y = list(map(int, input().split()))
if (x + y) % 3 != 0 or 2 * x < y or 2 * y < x:
print((0))
else:
x_min = (x + y) // 3
print((cmb((x + y) // 3, x - x_min, mod)))
if __name__ == "__main__":
setrecursionlimit(10000)
main()
| p02862 |
X, Y = list(map(int, input().split()))
mod = 10**9 + 7
if (X + Y) % 3 != 0 or X > 2*Y or Y > 2*X:
print((0))
else:
n2x = (2*X - Y) // 3
n1x = (2*Y - X) // 3
n = n2x + n1x
# nCn2xを求める
def combs(n,n2x):
invs = [1] * (n+1)
nfac = 1
for i in range(1, n+1):
nfac = nfac * i % mod
invs[i] = pow(nfac, mod-2, mod)
return nfac * invs[n2x] * invs[n-n2x] % mod
print((combs(n, n2x)))
| X, Y = list(map(int, input().split()))
mod = 10**9 + 7
if (X + Y) % 3 != 0 or X > 2*Y or Y > 2*X:
print((0))
else:
n2x = (2*X - Y) // 3
n1x = (2*Y - X) // 3
n = n2x + n1x
# nCn2xを求める
def combs(n,n2x,mod):
facs = [1] * (n+1)
# invs = [1] * (n+1)
nfac = 1
for i in range(1, n+1):
nfac = nfac * i % mod
facs[i] = nfac
# invs[i] = pow(nfac, mod-2, mod)
return nfac * (pow(facs[n2x], mod-2, mod) * pow(facs[n-n2x], mod-2, mod)) % mod
print((combs(n, n2x, mod))) | p02862 |
X,Y=list(map(int,input().split()))
def cmb(n, r, p):
if (r < 0) or (n < r):
return 0
r = min(r, n - r)
return fact[n] * factinv[r] * factinv[n-r] % p
p = 10 ** 9 + 7
N = 10 ** 6
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
for i in range(2, N + 1):
fact.append((fact[-1] * i) % p)
inv.append((-inv[p % i] * (p // i)) % p)
factinv.append((factinv[-1] * inv[-1]) % p)
if (X+Y)%3:
ans=0
else:
N=(X+Y)//3
if N<=X<=2*N and N<=Y<=2*N:
ans=cmb(N,X-N,p)
else:
ans=0
print(ans) | def com(n,r,m):
f=[1,1]
for i in range(2,n+1):
f.append(f[i-1]*i%m)
return f[n]*pow(f[r]*f[n-r]%m,m-2,m)%m
mod=10**9+7
x,y=list(map(int,input().split()))
z=(x+y)//3
if (x+y)%3 or abs(x-y)>z:
ans=0
else:
ans=com(z,x-z,mod)
print(ans) | p02862 |
import sys
input = sys.stdin.readline
def egcd(a, b):
if a == 0:
return b, 0, 1
else:
g, y, x = egcd(b % a, a)
return g, x - (b // a) * y, y
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def combination(n, r, mod=10**9+7):
r = min(r, n-r)
res = 1
for i in range(r):
res = res * (n - i) * modinv(i+1, mod) % mod
return res
X, Y = [int(x) for x in input().strip().split()]
p = (X, 2 * X)
n1 = X
n2 = 0
f = True
while p != (X, Y):
n1 -= 2
n2 += 1
p = (n1 + 2 * n2, 2 * n1 + n2)
if p[1] <= 0:
f = False
break
if n1 < 0 or n2 < 0:
print((0))
else:
print((combination(n1 + n2, n1) % (10 ** 9 + 7))) | import sys
input = sys.stdin.readline
def egcd(a, b):
if a == 0:
return b, 0, 1
else:
g, y, x = egcd(b % a, a)
return g, x - (b // a) * y, y
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def combination(n, r, mod=10**9+7):
r = min(r, n-r)
res = 1
for i in range(r):
res = res * (n - i) * modinv(i+1, mod) % mod
return res
X, Y = [int(x) for x in input().strip().split()]
p = (X, 2 * X)
n1 = X
n2 = 0
f = True
while p != (X, Y):
n1 -= 2
n2 += 1
p = (n1 + 2 * n2, 2 * n1 + n2)
if p[1] <= 0:
f = False
break
if n1 < 0 or n2 < 0:
print((0))
else:
print((combination(n1 + n2, n1))) | p02862 |
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
x,y=list(map(int,input().split()))
if (2*y-x)%3==0:
a=(2*y-x)//3
b=(2*x-y)//3
mod = 10**9+7 #出力の制限
N = a+b
r=min(a,b)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 )
print((cmb(N,r,mod)))
else:
print((0)) | def cmb(n,r,mod):
r=min(r,n-r)
if r==0:
return 1
elif r<0:
return 0
else:
X=1
Y=1
for i in range(r):
X*=n-i
X%=mod
Y*=i+1
Y%=mod
Y=pow(Y,mod-2,mod)
X*=Y
return X%mod
if __name__ == "__main__":
X,Y=list(map(int,input().split()))
if (2*Y-X)%3!=0 or (2*X-Y)%3!=0:
print((0))
else:
xd=(2*X-Y)//3
yd=(2*Y-X)//3
print((cmb(xd+yd,yd,10**9+7))) | p02862 |
x, y = list(map(int, input().split()))
if (x + y)%3 != 0:
print((0))
else:
k = (x + y)//3
if k <= x <= 2*k:
MOD = 10**9 + 7
fac = [0]*(k + 1)
finv = [0]*(k + 1)
inv = [0]*(k + 1)
fac[0] = 1; fac[1] = 1; finv[0] =1; finv[1] = 1; inv[1] = 1
for i in range(2, k + 1):
fac[i] = fac[i - 1] * i % MOD
inv[i] = MOD - inv[MOD%i] * (MOD // i) % MOD
finv[i] = finv[i - 1] * inv[i] % MOD
i = x - k
print((fac[k] * (finv[i] * finv[k - i] % MOD) % MOD))
else:
print((0)) | # 拡張ユークリッド互除法を用いて逆元を求める
def modinv(a, m):
b = m; x0 = 1; x1 = 0
while b:
q = a//b
a, b = b, a%b
x0, x1 = x1, x0 - q*x1
return x0%m
x, y = list(map(int, input().split()))
if (x + y)%3 != 0:
print((0))
else:
k = (x + y)//3
if k <= x <= 2*k:
i = min(x - k, 2*k - x)
# 結局 コンビネーションkCiに帰着
MOD = 10**9 + 7
# まず階乗のmodを求める
fac = [1]*(k + 1)
for j in range(2, k + 1):
fac[j] = fac[j - 1]*j%MOD
# 次に階乗の逆元を求める
finv = [0]*(k + 1)
#finv[k] = pow(fac[k], MOD - 2, MOD) # fac[k]の逆元, フェルマーの小定理
finv[k] = modinv(fac[k], MOD)
for j in range(k, i, - 1):
finv[j - 1] = finv[j]*j%MOD
print((fac[k] * (finv[i] * finv[k - i] % MOD) % MOD))
else:
print((0)) | p02862 |
# D - Knight
X, Y = list(map(int, input().split()))
####
a = (2*Y - X) / 3
b = (2*X - Y) / 3
# https://qiita.com/derodero24/items/91b6468e66923a87f39f
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] % mod * g2[n-r] % mod
mod = 10**9+7 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 )
if a%1 != 0 or b%1 != 0:
print((0))
else:
ans = cmb(int(a+b), int(min(a,b)), mod)
print(ans)
| # D - Knight
X, Y = list(map(int, input().split()))
####
a = (2*Y - X) / 3
b = (2*X - Y) / 3
# https://qiita.com/derodero24/items/91b6468e66923a87f39f
# を一部修正
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] % mod * g2[n-r] % mod
mod = 10**9+7 #出力の制限
N = int(a+b)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
if a%1 != 0 or b%1 != 0:
print((0))
else:
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 )
ans = cmb(int(a+b), int(min(a,b)), mod)
print(ans)
| p02862 |
mod = 10**9+7
def pow(n, x):
if x == 0:
return 1
elif x % 2 == 0:
return pow(n * n % mod, x // 2)
else:
return n * pow(n * n % mod, x // 2) % mod
def comb(n, r):
p, q = 1, 1
for i in range(r):
p = p * (n-i) % mod
q = q * (i+1) % mod
return p * pow(q, mod-2) % mod
x, y = list(map(int, input().split()))
m = abs(x - y)
n = (x + y) // 3
if (x + y) % 3 == 0 and n >= m:
print((comb(n, (n + m) // 2)))
else:
print((0)) | mod = 10**9+7
def comb(n, r):
p, q = 1, 1
for i in range(r):
p = p * (n-i) % mod
q = q * (i+1) % mod
return p * pow(q, mod-2, mod) % mod
x, y = list(map(int, input().split()))
m = abs(x - y)
n = (x + y) // 3
if (x + y) % 3 == 0 and n >= m:
print((comb(n, (n - m) // 2)))
else:
print((0)) | p02862 |
X,Y=list(map(int,input().split()))
import sys
if (2*Y-X)%3!=0 or (2*X-Y)%3!=0:
print((0))
sys.exit()
if (2*Y-X)<0 or (2*X-Y)<0:
print((0))
sys.exit()
x=(2*Y-X)//3
y=(2*X-Y)//3
#(x+y)Cxを求める
fac=[0 for i in range(x+y+1)]
inv=[0 for i in range(x+y+1)]
finv=[0 for i in range(x+y+1)]
#初期条件
p=1000000007
fac[0]=fac[1]=1
inv[1]=1
finv[0]=finv[1]=1
#テーブルの作成
for i in range(2,x+y+1):
fac[i]=fac[i-1]*i%p
#p=(p//a)*a+(p%a) a^(-1)=-(p//a)*(p%a)^(-1)
inv[i]=(-(p//i)*inv[p%i])%p
finv[i]=finv[i-1]*inv[i]%p
#求める
print(((fac[x+y]*finv[x]%p)*finv[y]%p))
| #(i,j)→（i+1,j+2）をx回、(i,j)→（i+2,j+1）がy回あるとすると
#x=(2Y-X)//3,y=(2X-Y)//3、となる
#これが整数or非負なら(x+y)Cxを求めればいい
X,Y=list(map(int,input().split()))
import sys
if (2*Y-X)%3!=0 or (2*X-Y)%3!=0:
print((0))
sys.exit()
if (2*Y-X)<0 or (2*X-Y)<0:
print((0))
sys.exit()
#それ以外なら存在する
x=(2*Y-X)//3
y=(2*X-Y)//3
#(x+y)Cxを求める
fac=[0 for i in range(x+y+1)]
inv=[0 for i in range(x+y+1)]
finv=[0 for i in range(x+y+1)]
#初期条件
fac[0]=fac[1]=1
inv[1]=1
finv[0]=finv[1]=1
p=1000000007
for i in range(2,x+y+1):
fac[i]=(fac[i-1]*i)%p
#p=(p//a)*a+(p%a) pの世界で a^(-1)=-(p//a)*inv[p%a]
inv[i]=(-(p//i)*inv[p%i])%p
finv[i]=(finv[i-1]*inv[i])%p
print(((fac[x+y]*finv[x]%p)*finv[y]%p))
| p02862 |
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def modfact(n):
fact=[1]*(n+1)
invfact=[1]*(n+1)
for i in range(1,n+1):
fact[i]=i*fact[i-1]%MOD
invfact[n]=pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
invfact[i]=invfact[i+1]*(i+1)%MOD
return fact,invfact
def resolve():
x,y=list(map(int,input().split()))
if((x+y)%3):
print((0))
return
z=(x+y)//3
if(x-z<0 or y-z<0):
print((0))
return
fact,invfact=modfact(z)
print((fact[z]*invfact[x-z]%MOD*invfact[y-z]%MOD))
resolve() | import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
class modfact(object):
def __init__(self,n):
fact=[1]*(n+1)
invfact=[1]*(n+1)
for i in range(1,n+1):
fact[i]=i*fact[i-1]%MOD
invfact[n]=pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
invfact[i]=invfact[i+1]*(i+1)%MOD
self.__fact=fact
self.__invfact=invfact
def fact(self,n):
return self.__fact[n]
def invfact(self,n):
return self.__invfact[n]
def comb(self,n,k):
if(k<0 or n-k<0): return 0
return (self.fact(n)*self.invfact(k)*self.invfact(n-k))%MOD
def resolve():
x,y=list(map(int,input().split()))
if((x+y)%3):
print((0))
return
z=(x+y)//3
mf=modfact(z)
print((mf.comb(z,x-z)))
resolve() | p02862 |
[x,y]=list(map(int,input().split()))
if ((x%3)+(y%3))%3!=0:
print((0))
else:
n=int((x+y)/3)
r=y-n
if r<0 or r>n:
print((0))
else:
if r>n-r:
r=n-r
mod=1000000007
kaijo=[1]
for i in range(1,n+1):
kaijo.append(kaijo[-1]*i%mod) #これで、kaijo[i]=i!となる。
gyakugen=[pow(kaijo[n-r],mod-2,mod)]
for i in reversed(list(range(1,n-r+1))):
gyakugen.append(gyakugen[-1]*i%mod) #これで、gyakugen[i]=n-r-iの逆元となる
kotae=kaijo[n]*gyakugen[0]*gyakugen[n-2*r]%mod
print(kotae) | [x,y]=list(map(int,input().split()))
#nCrのmodを求める
def nCrmod(n,r,mod):
if r<0 or r>n:
ans=0
else:
if r>n-r:
r=n-r
kaijo=[1] #階乗リスト作成
for i in range(1,n+1):
kaijo.append(kaijo[-1]*i%mod) #これで、kaijo[i]≡i!となる。
gyakugen=[pow(kaijo[n-r],mod-2,mod)] #逆限リスト作成
for i in reversed(list(range(1,n-r+1))):
gyakugen.append(gyakugen[-1]*i%mod) #これで、gyakugen[i]=n-r-iの逆元 となる。
ans=kaijo[n]*gyakugen[0]*gyakugen[n-2*r]%mod
return(ans)
if ((x%3)+(y%3))%3!=0:
print((0))
else:
n=int((x+y)/3)
r=y-n
mod=1000000007
print((nCrmod(n,r,mod))) | p02862 |
X,Y = list(map(int, input().split()))
class Combination:
"""
O(n)の前計算を1回行うことで，O(1)でnCr mod mを求められる
n_max = 10**6のとき前処理は約950ms (PyPyなら約340ms, 10**7で約1800ms)
使用例：
comb = Combination(1000000)
print(comb(5, 3)) # 10
"""
def __init__(self, n_max, mod=10**9+7):
self.mod = mod
self.modinv = self.make_modinv_list(n_max)
self.fac, self.facinv = self.make_factorial_list(n_max)
def __call__(self, n, r):
return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod
def make_factorial_list(self, n):
# 階乗のリストと階乗のmod逆元のリストを返す O(n)
# self.make_modinv_list()が先に実行されている必要がある
fac = [1]
facinv = [1]
for i in range(1, n+1):
fac.append(fac[i-1] * i % self.mod)
facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
return fac, facinv
def make_modinv_list(self, n):
# 0からnまでのmod逆元のリストを返す O(n)
modinv = [0] * (n+1)
modinv[1] = 1
for i in range(2, n+1):
modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
return modinv
if (X+Y) % 3 > 0:
print((0))
exit(0)
K = (X+Y)//3
if X < K or Y < K:
print((0))
exit(0)
comb = Combination(int(1e6+10))
print((comb(K, X-K))) | X,Y = list(map(int, input().split()))
class Combination:
"""
O(n)の前計算を1回行うことで，O(1)でnCr mod mを求められる
n_max = 10**6のとき前処理は約950ms (PyPyなら約340ms, 10**7で約1800ms)
使用例：
comb = Combination(1000000)
print(comb(5, 3)) # 10
"""
def __init__(self, n_max, mod=10**9+7):
self.mod = mod
self.modinv = self.make_modinv_list(n_max)
self.fac, self.facinv = self.make_factorial_list(n_max)
def __call__(self, n, r):
return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod
def make_factorial_list(self, n):
# 階乗のリストと階乗のmod逆元のリストを返す O(n)
# self.make_modinv_list()が先に実行されている必要がある
fac = [1]
facinv = [1]
for i in range(1, n+1):
fac.append(fac[i-1] * i % self.mod)
facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
return fac, facinv
def make_modinv_list(self, n):
# 0からnまでのmod逆元のリストを返す O(n)
modinv = [0] * (n+1)
modinv[1] = 1
for i in range(2, n+1):
modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
return modinv
if (X+Y) % 3 > 0:
print((0))
exit(0)
K = (X+Y)//3
if X < K or Y < K:
print((0))
exit(0)
comb = Combination(K+10)
print((comb(K, X-K))) | p02862 |
x, y = list(map(int, input().split()))
MOD = int(1.0e+9 + 7)
DP_max = 3333334
DP = []
X = int((2 * y - x) / 3)
Y = int((2 * x - y) / 3)
def cmb(n, r, p):
if (r < 0) or (n < r):
return 0
r = min(r, n - r)
return fact[n] * factinv[r] * factinv[n-r] % p
p = 10 ** 9 + 7
N = 10 ** 6 # N は必要分だけ用意する
fact = [1, 1] # fact[n] = (n! mod p)
factinv = [1, 1] # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1] # factinv 計算用
for i in range(2, N + 1):
fact.append((fact[-1] * i) % p)
inv.append((-inv[p % i] * (p // i)) % p)
factinv.append((factinv[-1] * inv[-1]) % p)
if((2 * y - x) % 3 != 0 or (2 * x - y) % 3 != 0 or
(2 * y - x) < 0 or (2 * x - y) < 0):
print((0))
else:
print((cmb(X + Y, Y, MOD))) | x, y = list(map(int, input().split()))
def cmb(n, r, mod):
if (r < 0) or (n < r):
return 0
r = min(r, n - r)
return fact[n] * factinv[r] * factinv[n-r] % mod
X = int((2 * y - x) / 3)
Y = int((2 * x - y) / 3)
MOD = int(1.0e+9 + 7)
N = int(7.0e+5) # N は必要分だけ用意する
fact = [1, 1] # fact[n] = (n! mod p)
factinv = [1, 1] # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1] # factinv 計算用
for i in range(2, N + 1):
fact.append((fact[-1] * i) % MOD)
inv.append((-inv[MOD % i] * (MOD // i)) % MOD)
factinv.append((factinv[-1] * inv[-1]) % MOD)
if((2 * y - x) % 3 != 0 or (2 * x - y) % 3 != 0 or
(2 * y - x) < 0 or (2 * x - y) < 0):
print((0))
else:
print((cmb(X + Y, Y, MOD))) | p02862 |
import math
a,b=list(map(int,input().split()))
x=max(a,b)
y=min(a,b)
p=abs(x-y)
P = 10**9 + 7
N = 1000000
inv_t = [0]+[1]
for i in range(2,N):
inv_t += [inv_t[P % i] * (P - int(P / i)) % P]
if (x+y)%3!=0:
print((0))
elif x>y*2:
print((0))
else:
n=(x+y)//3
q=(2*x-y)//3
r=(2*y-x)//3
#print(math.factorial(q+r)//math.factorial(q)//math.factorial(r)%(10**9+7))
ans=1
qq=1
rr=1
for i in range(1,q+r+1):
ans*=i
ans%=10**9+7
for i in range(1,q+1):
ans*=inv_t[i]
ans%=10**9+7
P = 10**9 + 7
N = r+2
inv_t = [0]+[1]
for i in range(2,N):
inv_t += [inv_t[P % i] * (P - int(P / i)) % P]
for i in range(1,r+1):
ans*=inv_t[i]
ans%=10**9+7
print(ans)
| import math
a,b=list(map(int,input().split()))
x=max(a,b)
y=min(a,b)
p=abs(x-y)
if (x+y)%3!=0:
print((0))
elif x>y*2:
print((0))
else:
n=(x+y)//3
q=(2*x-y)//3
r=(2*y-x)//3
#print(math.factorial(q+r)//math.factorial(q)//math.factorial(r)%(10**9+7))
ans=1
qq=1
rr=1
P = 10**9 + 7
N = max(q,r)+2
inv_t = [0]+[1]
for i in range(2,N):
inv_t += [inv_t[P % i] * (P - int(P / i)) % P]
for i in range(1,q+r+1):
ans*=i
ans%=10**9+7
for i in range(1,q+1):
ans*=inv_t[i]
ans%=10**9+7
for i in range(1,r+1):
ans*=inv_t[i]
ans%=10**9+7
print(ans)
| p02862 |
import sys
input = sys.stdin.readline
MOD = 1000000007
def comb_mod(n, r, mod):
if n < r:
return 0
elif n < 0 or r < 0:
return 0
else:
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]
for i in range(2, n + 1):
fac.append(fac[-1] * i % mod)
inv.append(-inv[mod % i] * (mod // i) % mod)
finv.append((finv[-1] * inv[-1]) % mod)
return int(fac[n] * finv[r] * finv[n - r] % mod)
x, y = list(map(int, input().split()))
m = int((x * 2 - y) / 3)
n = int(x - 2 * m)
if (x + y) % 3 != 0:
print((0))
else:
print((comb_mod(n + m, n, MOD)))
| import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7
class CmbMod:
def __init__(self, n, p):
"""
二項係数nCr(n個の区別できるものからr個のものを選ぶ組み合わせの数)をpで割った余りを求める
"""
self.n = n
self.p = p
self.fact = [1, 1]
self.factinv = [1, 1]
self.inv = [0, 1]
def cmb_mod(self, n, r):
"""
二項係数nCr(mod p)をO(r)にて計算。nが大きいがrは小さい時に使用。
"""
numer, denom = 1, 1
for i in range(r):
numer = (numer * (n - i)) % self.p
denom = (denom * (i + 1)) % self.p
return (numer * pow(denom, self.p - 2, self.p)) % self.p
def prep(self):
"""
二項係数nCr(mod p)をO(1)で求める為の前処理をO(N)にて実行。
"""
for i in range(2, self.n + 1):
self.fact.append((self.fact[-1] * i) % self.p)
self.inv.append((-self.inv[self.p % i] * (self.p // i)) % self.p)
self.factinv.append((self.factinv[-1] * self.inv[-1]) % self.p)
def cmb_mod_with_prep(self, n, r):
"""
二項係数nCr(mod p)をO(1)で求める。事前にprepを実行する事。
"""
if (r < 0) or (n < r):
return 0
r = min(r, n - r)
return self.fact[n] * self.factinv[r] * self.factinv[n - r] % self.p
def resolve():
X, Y = list(map(int, input().split()))
cnt = (X + Y) // 3
left = 0
right = 0
for i in range(cnt):
if (i * 1 + (cnt - i) * 2 == X and i * 2 + (cnt - i) * 1 == Y) or (
i * 1 + (cnt - i) * 2 == Y and i * 2 + (cnt - i) * 1 == X):
left = i
right = cnt - i
break
else:
print((0))
exit()
cmb = CmbMod(cnt, mod)
res = cmb.cmb_mod(cnt, min(left, right))
print(res)
if __name__ == '__main__':
resolve()
| p02862 |
import math
X,Y = list(map(int,input().split()))
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
nCr={}
def cmb(n, r):
if n - r < r: r = n - r
if r == 0: return 1
if r == 1: return n
numerator = [n - r + k + 1 for k in range(r)]
denominator = [k + 1 for k in range(r)]
for p in range(2,r+1):
pivot = denominator[p - 1]
if pivot > 1:
offset = (n - r) % p
for k in range(p-1,r,p):
numerator[k - offset] /= pivot
denominator[k] /= pivot
result = 1
for k in range(r):
if numerator[k] > 1:
result *= int(numerator[k])
return result
def count():
if not (a//1 == a and b//1==b):
return 0
else:
ahat = int(a%n)
bhat = int(b%n)
return cmb(ahat+bhat,ahat)
print((int(count())%(10**9+7))) | import math
X,Y = list(map(int,input().split()))
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
def cmb(n, r, mod=10**9+7):
n1, r = n+1, min(r, n-r)
numer = denom = 1
for i in range(1, r+1):
numer = numer * (n1-i) % mod
denom = denom * i % mod
return numer * pow(denom, mod-2, mod) % mod
def count():
if not (a//1 == a and b//1==b):
return 0
else:
ahat = int(a%n)
bhat = int(b%n)
return cmb(ahat+bhat,ahat)
print((int(count())%(10**9+7))) | p02862 |
def comb(n, k, MOD):
if n < k or n < 0 or k < 0:
return 0
k = min(k, n - k)
if k == 0:
return 1
iinv = [1] * (k + 1)
ans = n
for i in range(2, k + 1):
iinv[i] = MOD - iinv[MOD % i] * (MOD // i) % MOD
ans *= (n + 1 - i) * iinv[i] % MOD
ans %= MOD
return ans
mm = 10**9 + 7
x, y = (int(x) for x in input().split())
ans = 0
if (x - 2*y) % 3 == 0:
beta = (x - 2*y) // -3
alpha = y - 2*beta
ans = comb(alpha+beta, beta, mm)
print(ans) | # https://www.geeksforgeeks.org/compute-ncr-p-set-3-using-fermat-little-theorem/
def comb(n, r, p):
num = den = 1
for i in range(r):
num = (num * (n - i)) % p
den = (den * (i + 1)) % p
return (num * pow(den, p - 2, p)) % p
m = 10**9 + 7
x, y = (int(x) for x in input().split())
ans = 0
if (x - 2*y) % 3 == 0:
beta = (x - 2*y) // -3
alpha = y - 2*beta
ans = comb(alpha+beta, max(alpha, beta), m)
print(ans) | p02862 |
X,Y=list(map(int,input().split()))
if (X+Y)%3!=0:
print((0))
exit()
A=int((X+Y)/3)
B=int((2*Y-X)/3)
if A<0 or B<0:
print((0))
exit()
MOD=10**9+7
def comb(n,k):
tmp=1
for i in range(n-k+1,n+1):
tmp*=i
tmp%=MOD
for i in range(1,k+1):
tmp*=pow(i,MOD-2,MOD)
tmp%=MOD
return tmp
ans = comb(A,B)
print((ans%MOD)) | #ika tako
def prepare(n, MOD):
f = 1
for m in range(1, n + 1):
f = f * m % MOD
#print(f)
fn = f#n!を求める
#print(fn)
#print(f)
inv = pow(f, MOD - 2, MOD)
#print(inv)
invs = [1] * (n + 1)#[1, 1, 1]のイメージ、逆元？格納テーブル
#print(invs) ⇒ [1, 1, 1]のイメージ、逆元格納テーブル
invs[n] = inv
for m in range(n, 1, -1):#n*(n-1)*(n-2)*...と上から掛けている
inv = inv * m % MOD#なぜ、下から掛けない？
invs[m - 1] = inv
return fn, invs
def solve(x, y):
d, m = divmod(x + y, 3)#商と余り
if m != 0 or x < d or y < d:
#Xとyの合計は3の倍数、x、yがd移動回数以下はあり得ない（1回1個は進む）
return 0
#c = d - x これだと範囲外参照でエラー
c = abs(d - x)
MOD = 10 ** 9 + 7
f, invs = prepare(d, MOD)
return f * invs[c] * invs[d - c] % MOD
#fはn!、invs[c],invs[d - c] はc!,(d-c)!の逆元？
#nCr=n!/(r!*(n-r)!)
x, y = list(map(int, input().split()))
print((solve(x, y))) | p02862 |
'''
Aは移動関数と同数：xとy方向に合計で3進んでいるから
Bは移動回数の内、(i+1,j+2)を選んだ回数：
1回でx方向には1進み、y方向には2進む
進み方は2通りしかないので、全体の内、1通りを選んだ回数を求めればOK
'''
X,Y=list(map(int,input().split()))
if (X+Y)%3!=0:#まず、条件に合わないケースを除外
print((0))
exit()
A=int((X+Y)/3)
B=int((2*Y-X)/3)
if A<0 or B<0:
print((0))
exit()
MOD=10**9+7
def comb(n,k):#組合せを求める関数
tmp=1
for i in range(n-k+1,n+1):#分子：n*(n-1)*...*(n-k+1)
tmp*=i
tmp%=MOD
for i in range(1,k+1):#分母：k!
tmp*=pow(i,MOD-2,MOD)#分母なので逆元にする
tmp%=MOD
return tmp
ans = comb(A,B)#上記説明の通り。要は組み合わせの問題
print((ans%MOD)) | #ika tako
'''
A.ダメなケースを除外できるか、B.組合せの数を問題に応じて求められるか
階乗や逆元はfor文で求める。
ダメなケースを除外した上で、最終X,Y に行くには、二つの選択肢
(i+1,j+2),(i+2,j+1)の組合せの数を求める。
組合せの数を求める時は、階乗と逆元を使う。
逆元は一通り、全て求めておいて、配列invsに格納して、後で使う。
'''
def prepare(n, MOD):
f = 1
for m in range(1, n + 1):
f = f * m % MOD
fn = f#n!を求める
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)#[1, 1, 1]のイメージ、逆元？格納テーブル
invs[n] = inv#配列の一番最後のデータ
for m in range(n, 1, -1):#n*(n-1)*(n-2)*...と上から掛けている
inv = inv * m % MOD#逆元を一通り、求めて、配列invsに格納する
invs[m - 1] = inv
return fn, invs
def solve(x, y):#ダメなケースの除外
d, m = divmod(x + y, 3)#商と余り
if m != 0 or x < d or y < d:
#Xとyの合計は3の倍数、x、yがd移動回数以下はあり得ない（1回1個は進む）
return 0
#c = d - x これだと範囲外参照でエラー
c = abs(d - x)#nCr=nC(n-r)、Cの後ろのrと(n-r)を入れ替えても同じ
MOD = 10 ** 9 + 7
f, invs = prepare(d, MOD)
return f * invs[c] * invs[d - c] % MOD
#fはn!、invs[c],invs[d - c] はc!,(d-c)!の逆元？
#nCr=n!/(r!*(n-r)!)
x, y = list(map(int, input().split()))
print((solve(x, y))) | p02862 |
MOD = 10 ** 9 + 7
def power_expo(x, y):
"""Returns x^y.
<https://qiita.com/Yaruki00/items/fd1fc269ff7fe40d09a6>
結局, 組み込み関数の `pow()` のほうが速そう. 第3引数でmodもできる.
"""
if y == 0:
return 1
elif y % 2 == 0:
return power_expo(x, y // 2) ** 2 % MOD
else:
return power_expo(x, y // 2) ** 2 * x % MOD
def main():
x, y = [int(x) for x in input().split()]
if (x + y) % 3 != 0:
return 0
summ = (x + y) // 3 # d + r
diff = x - y # d - r
if summ % 2 != diff % 2:
return 0
d = (summ + diff) // 2 # Down
r = (summ - diff) // 2 # Right
if d < 0 or r < 0:
return 0
chosen = min(d, r)
patterns = 1
for i, j in zip(list(range(summ - chosen + 1, summ + 1)), list(range(1, summ + 1))):
patterns = patterns % MOD * i % MOD * pow(j, MOD - 2, MOD) % MOD
return patterns
if __name__ == '__main__':
print((main()))
# やはり難しい，再び解説。割り算のときは mod 10^9+7 が厄介。
# とりあえず，割る方は 10^9+5 乗して掛ければいいらしい。
| MOD = 10 ** 9 + 7
def power_expo(x, y):
"""Returns x^y.
<https://qiita.com/Yaruki00/items/fd1fc269ff7fe40d09a6>
結局, 組み込み関数の `pow()` のほうが速そう. 第3引数でmodもできる.
"""
if y == 0:
return 1
elif y % 2 == 0:
return power_expo(x, y // 2) ** 2 % MOD
else:
return power_expo(x, y // 2) ** 2 * x % MOD
def combinations_mod(n, r, mod=1000000007):
"""Returns nCr in mod."""
combs = 1
for i, j in zip(list(range(n - r + 1, n + 1)), list(range(1, r + 1))):
combs = combs % mod * i % mod * pow(j, mod - 2, mod) % mod
return combs
def main():
x, y = [int(x) for x in input().split()]
if (x + y) % 3 != 0:
return 0
summ = (x + y) // 3 # d + r
diff = x - y # d - r
if summ % 2 != diff % 2:
return 0
d = (summ + diff) // 2 # Down
r = (summ - diff) // 2 # Right
if d < 0 or r < 0:
return 0
chosen = min(d, r)
patterns = combinations_mod(summ, chosen)
return patterns
if __name__ == '__main__':
print((main()))
# やはり難しい，再び解説。割り算のときは mod 10^9+7 が厄介。
# とりあえず，割る方は 10^9+5 乗して掛ければいいらしい。
# でかい累乗, pow() なら間に合うな. Python3 1310 ms; Pypy3 457 ms.
| p02862 |
import sys
mod=10**9+7
x,y=list(map(int,input().split()))
a=(-x+2*y)//3
b=(2*x-y)//3
if a<0 or b<0:
print((0))
sys.exit()
f=[1]
for i in range(1,a+b+1):
f.append(f[-1]*i%mod)
if a+2*b==x and 2*a+b==y:
print((f[a+b]*pow(f[a]*f[b],mod-2,mod)%mod))
else:
print((0)) | import sys
mod=10**9+7
x,y=list(map(int,input().split()))
a=(-x+2*y)//3
b=(2*x-y)//3
if a<0 or b<0:
print((0))
sys.exit()
f=[1]
for i in range(1,a+b+1):
f.append(f[-1]*i%mod)
if a+2*b==x and 2*a+b==y:
print((f[a+b]*pow(f[a],mod-2,mod)*pow(f[b],mod-2,mod)%mod))
else:
print((0)) | p02862 |
X,Y = list(map(int,input().split()))
if (X+Y)%3 != 0 or X > 2*Y or Y > 2*X:
print((0))
else:
ab = (X+Y)//3
a = X - ab
b = ab - a
mod = 10**9+7
def cmb(n, r, mod):
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 #出力の制限
N = 10**6+1
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 )
ans = cmb(ab,b,mod)
print(ans) | X,Y = list(map(int,input().split()))
def comb(n,k,p):
"""power_funcを用いて(nCk) mod p を求める"""
from math import factorial
if n<0 or k<0 or n<k: return 0
if n==0 or k==0: return 1
a = 1
b = 1
c = 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*power_func(b,p-2,p)*power_func(c,p-2,p))%p
def power_func(a,b,p):
"""a^b mod p を求める"""
if b==0: return 1
if b%2==0:
d=power_func(a,b//2,p)
return d*d %p
if b%2==1:
return (a*power_func(a,b-1,p ))%p
if (X+Y)%3 != 0 or X > 2*Y or Y > 2*X:
print((0))
else:
ab = (X+Y)//3
a = X - ab
b = ab - a
mod = 10**9+7
ans = comb(ab,min(a,b),mod)
print(ans) | p02862 |
X, Y = list(map(int, input().split()))
MOD = 10 ** 9 + 7
def modpow(a, n):
ret = 1
while n > 0:
if n & 1:
ret = ret * a % MOD
a = a * a % MOD
n >>= 1
return ret
def modinv(a):
return modpow(a, MOD - 2)
def modfac(x):
ret = 1
for i in range(2, x + 1):
ret *= i
ret %= MOD
return ret
ans = 0
if (X + Y) % 3 == 0:
a = (2 * X - Y) // 3
b = (2 * Y - X) // 3
if a >= 0 and b >= 0:
n = a + b
r = a
ans = modfac(n)
ans *= modinv(modfac(n - r) * modfac(r))
ans %= MOD
print(ans) | X, Y = list(map(int, input().split()))
MOD = 10 ** 9 + 7
def modpow(x, n):
ret = 1
while n > 0:
if n & 1:
ret = ret * x % MOD
x = x * x % MOD
n >>= 1
return ret
def modinv(x):
return modpow(x, MOD - 2)
def modf(x):
ret = 1
for i in range(2, x + 1):
ret *= i
ret %= MOD
return ret
ans = 0
if (X + Y) % 3 == 0:
m = (2 * X - Y) // 3
n = (2 * Y - X) // 3
if m >= 0 and n >= 0:
ans = modf(m + n) * modinv(modf(n) * modf(m))
ans %= MOD
print(ans) | p02862 |
def solve():
mod = 10 ** 9 + 7
x, y = list(map(int, input().split()))
sum_ = x + y
q, r = divmod(sum_, 3)
if r != 0:
return 0
a = (x * 2 - y) // 3
b = (y * 2 - x) // 3
if a < 0 or b < 0:
return 0
def cmb(n, r):
return (fact[n] * finv_t[r] * finv_t[n - r]) % mod
fact = [1, 1]
inv_t = [0, 1]
finv_t = [1, 1]
for i in range(2, q + 1):
fact.append((fact[-1] * i) % mod)
inv_t.append((-inv_t[mod % i] * (mod // i)) % mod)
finv_t.append((finv_t[-1] * inv_t[-1]) % mod)
return cmb(q, a)
print((solve()))
| def main():
mod = 10 ** 9 + 7
def choose(n, a, mod=mod):
x, y = 1, 1
for i in range(a):
x = x * (n - i) % mod
y = y * (i + 1) % mod
return x * pow(y, mod - 2, mod) % mod
x, y = list(map(int, input().split()))
q, r = divmod(x + y, 3)
if r != 0:
print((0))
return
# b:=(+2,+1)
d = x * 2 - y
if d < 0 or d % 3 != 0:
print((0))
return
b = d // 3
if q < b:
print((0))
return
res = choose(q, min(b, q - b), mod)
print(res)
if __name__ == '__main__':
main()
| p02862 |
X,Y=list(map(int,input().split()))
mod=10**9+7
def nCr(n, r, mod):
r = min(r, n-r)
numer = denom = 1
for i in range(1, r+1):
numer = numer * (n+1-i) % mod
denom = denom * i % mod
return numer * pow(denom, mod-2, mod) % mod
if (X+Y)%3 != 0:
print((0))
exit()
n,x,y=0,X,Y
while x != y*2:
x-=1
y-=2
n+=1
m=((X+Y)//3)-n
if n<0 or m<0:
print((0))
exit()
ans = nCr(n+m,n,mod)
print(ans)
| X,Y=list(map(int,input().split()))
mod=10**9+7
def nCr(n, r, mod):
r = min(r, n-r)
numer = denom = 1
for i in range(1, r+1):
numer = numer * (n+1-i) % mod
denom = denom * i % mod
return numer * pow(denom, mod-2, mod) % mod
if (X+Y)%3 != 0:
print((0))
exit()
n=((2*X)-Y)//3
m=((X+Y)//3)-n
if n<0 or m<0:
print((0))
exit()
ans = nCr(n+m,n,mod)
print(ans)
| p02862 |
class Solution:
def solve(self, x: int, y: int) -> int:
if (2*x - y) % 3 != 0 or (-x + 2*y) % 3 != 0:
return 0
m = (2*x - y) // 3
n = (-x + 2*y) // 3
if m < 0 or n < 0:
return 0
# calculate {m+n}C{n}
def egcd(a, b):
if a == 0:
return b, 0, 1
else:
g, y, x = egcd(b % a, a)
return g, x - (b // a) * y, y
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def convination(n: int, r: int, mod: int = 10**9+7) -> int:
r = min(r, n-r)
res = 1
for i in range(r):
res = res * (n-i) * modinv(i+1, mod) % mod
return res
return convination(n+m, m)
if __name__ == '__main__':
# standard input
x, y = list(map(int, input().split()))
# solve
solution = Solution()
print((solution.solve(x, y)))
| class MathUtil:
# calculate {m+n}C{n}
def egcd(self, a: int, b: int):
if a == 0:
return b, 0, 1
else:
g, y, x = self.egcd(b % a, a)
return g, x - (b // a) * y, y
def modinv(self, a: int, m: int):
g, x, y = self.egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def combination(self, n: int, r: int, mod: int = 10**9+7) -> int:
r = min(r, n-r)
res = 1
for i in range(r):
res = res * (n-i) * self.modinv(i+1, mod) % mod
return res
x, y = list(map(int, input().split()))
m = - x + 2*y
n = 2*x - y
if m % 3 != 0 or n % 3 != 0 or m < 0 or n < 0:
print((0))
else:
m //= 3
n //= 3
print((MathUtil().combination(m+n, n)))
| p02862 |
# nCrの左項には nn しか来ない場合、1!～(n-1)!は保持しなくてよいバージョン
def prepare(n, MOD):
# n! の計算
f = 1
for m in range(1, n+1):
f *= m
f %= MOD
fn = f
# n!^-1 の計算
inv = pow(f, MOD-2, MOD)
# n!^-1 - 1!^-1 の計算
invs = [1]*(n+1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m-1] = inv
return fn, invs
MOD = 10**9+7
x, y = list(map(int, input().split()))
d, m = divmod(x+y, 3)
if m != 0 or x/y > 2 or y/x > 2:
print((0))
exit()
c = abs(d-x)
f, invs = prepare(d, MOD)
ans = f * invs[c] * invs[d-c] % MOD
print(ans) | # nCr mod m
# rがn/2に近いと非常に重くなる
def combination(n, r, mod=10**9+7):
n1, r = n+1, min(r, n-r)
numer = denom = 1
for i in range(1, r+1):
numer = numer * (n1-i) % mod
denom = denom * i % mod
return numer * pow(denom, mod-2, mod) % mod
X, Y = list(map(int, input().split()))
if (X+Y) % 3 != 0 or not (X <= 2*Y and Y <= 2*X):
print((0))
exit()
n = (X+Y) // 3
r = Y - n
#print(n, r)
print((combination(n, r))) | p02862 |
# 法Pの下での組み合わせ数 nCk を求める
# MAX: nの最大値
P = (10**9)+7
fac=[]
inv=[]
finv=[]
# 拡張ユークリッドアルゴリズム
# (d, x, y): d=ax+by を満たすd, x, yを求める
# aとbが互いに素な整数であればgcd(a,b)=d=1, ax=1 (mod b)
# xは法bの元でaの乗法逆元a^-1になる
def exEuclid(a, b):
if (b==0):
return (a, 1, 0)
else:
(dd, xx, yy) = exEuclid(b, a % b)
return (dd, yy, xx - (a//b)*yy)
def COMinit(MAX):
global fac, inv, finv
fac=[1 for _ in range(MAX)]
inv=[1 for _ in range(MAX)]
finv=[1 for _ in range(MAX)]
#print('len(fac): {}'.format(len(fac)))
#print(MAX)
for i in range(2,MAX):
#print(i)
fac[i] = fac[i-1]*i % P
(d, x, y) = exEuclid(i, P)
inv[i] = x
finv[i] = finv[i-1]*inv[i] % P
def COM(n, k):
if(n<k):
return 0
elif ( (n<0)or(k<0)):
return 0
else:
return fac[n]*(finv[n-k]*finv[k] % P) % P
####
#print('x, y:')
x, y = list(map(int,input().split()))
MAX = (x+y)//3 +1 # (X+Y)/3より大きい整数 1 <= X, Y <= 10**6
COMinit(MAX)
if ((x+y)%3 != 0):
print((0))
exit()
else:
n1 = (-x+2*y)//3
n2 = (2*x -y)//3
if (n1<0):
print((0))
exit()
elif(n2<0):
print((0))
exit()
else:
npath = COM(n1+n2, n1)
print(npath)
| # 拡張ユークリッドアルゴリズム
# (d, x, y): d=ax+by を満たすd, x, yを求める
# aとbが互いに素な整数であればgcd(a,b)=d=1, ax=1 (mod b)
# xは法bの元でaの乗法逆元a^-1になる
def exEuclid(a, b):
if (b==0):
return (a, 1, 0)
else:
(dd, xx, yy) = exEuclid(b, a % b)
return (dd, yy, xx - (a//b)*yy)
def mycomb(n, k, p):
k = min(n-k,k)
fact=1
finv=1
for i in range(k):
fact=fact*(n-i) % p
finv=finv*(i+1) % p
(d, x, y) = exEuclid(finv, p)
return fact*x % p
x, y = list(map(int,input().split()))
if ((x+y)%3 != 0):
print((0))
exit()
else:
n1 = (-x+2*y)//3
n2 = (2*x -y)//3
if( (n1<0) or (n2<0) ):
print((0))
exit()
npath = mycomb(n1+n2, n2, 10**9+7)
print(npath)
| p02862 |
MOD = 10 ** 9 + 7
#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
r = [1,0,a]
w = [0,1,b]
while w[2]!=1:
q = r[2]//w[2]
r2 = w
w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
r = r2
w = w2
#[x,y]
return [w[0],w[1]]
# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
x = extgcd(a,m)[0]
return (m+x%m)%m
X, Y = list(map(int, input().split()))
if (X + Y) % 3 != 0:
print((0))
exit()
time = (X+Y) // 3
diff = X - Y
if abs(diff) > time:
print((0))
exit()
x_time = (time+diff) // 2
res = 1
for i in range(1,time+1):
res = res*i%MOD
for i in range(1,x_time+1):
res = res*mod_inv(i,MOD)%MOD
for i in range(1,time-x_time+1):
res = res*mod_inv(i, MOD)%MOD
print(res)
#print(mod_combination(time, x_time, MOD))
| def cmb(n, k, mod, fac, ifac):
# nCkを計算する
k = min(k, n-k)
return fac[n] * ifac[k] * ifac[n-k] % mod
def make_tables(mod, n):
# 階乗テーブル、逆元の階乗テーブルを作成する
fac = [1, 1] # 階乗テーブル
ifac = [1, 1] # 逆元の階乗テーブル
inverse = [0, 1] # 逆元テーブル 0の階乗は1
for i in range(2, n+1):
fac.append((fac[-1] * i) % mod)
inverse.append((-inverse[mod % i] * (mod//i)) % mod)
ifac.append((ifac[-1] * inverse[-1]) % mod)
return fac, ifac
X, Y = list(map(int, input().split()))
if X > Y:
X, Y = Y, X
dist = X + Y
if dist % 3 != 0:
print((0))
exit()
total = int((X+Y) / 3)
n = X - total
if Y > 2*X:
print((0))
else:
MOD = 10**9 + 7
fac, ifac = make_tables(MOD, total)
answer = cmb(total, n, MOD, fac, ifac)
print(answer)
"""
p = (p/a)×a + (p %a)
この両辺の mod p をとると、
(p/a)×a + (p%a) ≡ 0
⇔(p/a) + (p%a)×a−1 ≡ 0 (両辺に a−1 をかける)
⇔(p%a) × a−1 ≡ −(p/a)
⇔a−1 ≡ −(((p%a)^−1) × (p/a))
""" | p02862 |
def cmb(n, k, mod, fac, ifac):
# nCkを計算する
k = min(k, n-k)
return fac[n] * ifac[k] * ifac[n-k] % mod
def make_tables(mod, n):
# 階乗テーブル、逆元の階乗テーブルを作成する
fac = [1, 1] # 階乗テーブル
ifac = [1, 1] # 逆元の階乗テーブル
inverse = [0, 1] # 逆元テーブル 0の階乗は1
for i in range(2, n+1):
fac.append((fac[-1] * i) % mod)
inverse.append((-inverse[mod % i] * (mod//i)) % mod)
ifac.append((ifac[-1] * inverse[-1]) % mod)
return fac, ifac
X, Y = list(map(int, input().split()))
if X > Y:
X, Y = Y, X
dist = X + Y
if dist % 3 != 0:
print((0))
exit()
total = int((X+Y) / 3)
n = X - total
if Y > 2*X:
print((0))
else:
MOD = 10**9 + 7
fac, ifac = make_tables(MOD, total)
answer = cmb(total, n, MOD, fac, ifac)
print(answer)
"""
p = (p/a)×a + (p %a)
この両辺の mod p をとると、
(p/a)×a + (p%a) ≡ 0
⇔(p/a) + (p%a)×a−1 ≡ 0 (両辺に a−1 をかける)
⇔(p%a) × a−1 ≡ −(p/a)
⇔a−1 ≡ −(((p%a)^−1) × (p/a))
""" | import sys
sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))
def cmb(n, k, mod, fac, ifac):
# nCkを計算する
k = min(k, n-k)
return fac[n] * ifac[k] * ifac[n-k] % mod
def make_tables(mod, n):
# 階乗テーブル、逆元の階乗テーブルを作成する
fac = [1, 1] # 階乗テーブル
ifac = [1, 1] # 逆元の階乗テーブル
inverse = [0, 1] # 逆元テーブル 0の階乗は1 0の逆元は0
for i in range(2, n+1):
fac.append((fac[-1] * i) % mod)
inverse.append((-inverse[mod % i] * (mod//i)) % mod)
ifac.append((ifac[-1] * inverse[-1]) % mod)
return fac, ifac
X, Y = lr()
MOD = 10 ** 9 + 7
if (X+Y)%3 != 0 or X > 2 * Y or Y > 2 * X:
print((0))
exit()
if X < Y:
X, Y = Y, X
# Xが大きい
total_time = (X+Y)//3
x_time = (X - Y + total_time) // 2
# total_time C i_time
fac, ifac = make_tables(MOD, total_time)
answer = fac[total_time] * ifac[x_time] * ifac[total_time - x_time] % MOD
print(answer)
# 44 | p02862 |
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf,comb
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT() : return int(eval(input()))
def MAP() : return list(map(int,input().split()))
def LIST() : return list(MAP())
def cmb(n, r, mod):
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 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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()
a = 2*x - y
b = 2*y - x
if a >= 0 and b >= 0 and a % 3 == 0 and b % 3 == 0:
a //= 3
b //= 3
ans = cmb(a+b, a, 10**9+7)
else:
ans = 0
print(ans) | from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf,comb
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT() : return int(eval(input()))
def MAP() : return list(map(int,input().split()))
def LIST() : return list(MAP())
def mycmb(n,r,p):
r = min(r,n-r)
if r == 0:
return 1
over = reduce(lambda x,y:x*y%p,list(range(n,n-r,-1)))
under = reduce(lambda x,y:x*y%p,list(range(1,r+1)))
return (over * pow(under,p-2,p))%p
x, y = MAP()
a = 2*x - y
b = 2*y - x
if a >= 0 and b >= 0 and a % 3 == 0 and b % 3 == 0:
a //= 3
b //= 3
ans = mycmb(a+b, a, 10**9+7)
else:
ans = 0
print(ans) | p02862 |
class ModComb:
def __init__(self, MAX, mod=10 ** 9 + 7):
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]
for i in range(2, MAX):
fac.append(fac[i - 1] * i % mod)
inv.append(mod - inv[mod % i] * (mod // i) % mod)
finv.append(finv[i - 1] * inv[i] % mod)
self.fac, self.finv, self.mod = fac, finv, mod
def nCk(self, n, k):
if n < k or n < 0 or k < 0:
return 0
fac, finv, mod = self.fac, self.finv, self.mod
return fac[n] * (finv[k] * finv[n - k] % mod) % mod
mod = 10 ** 9 + 7
mc = ModComb(3 * 10 ** 6, mod)
X, Y = list(map(int, input().split()))
if (2 * X - Y) % 3 != 0 or (X - 2 * Y) % 3 != 0:
print((0))
quit()
b = (2 * X - Y) // 3
a = (-X + 2 * Y) // 3
print((mc.nCk(a + b, a))) | def nCk(n, k, mod=10 ** 9 + 7):
def xgcd(a, b):
if b == 0:
return (a, 1, 0)
g, x, y = xgcd(b, a % b)
return (g, y, x - (a // b) * y)
p, q = 1, 1
for i in range(n - k + 1, n + 1):
p = (p * i) % mod
for i in range(2, k + 1):
q = (q * i) % mod
return p * (xgcd(q, mod)[1] % mod) % mod
X, Y = list(map(int, input().split()))
b = (2 * X - Y) // 3
a = (-X + 2 * Y) // 3
if (X + Y) % 3 != 0 or a < 0 or b < 0:
print((0))
else:
print((nCk(a + b, a))) | p02862 |
def main():
def nCk(n, k, mod=10 ** 9 + 7):
def xgcd(a, b):
if b == 0:
return (1, 0)
x, y = xgcd(b, a % b)
return (y, x - (a // b) * y)
p, q = 1, 1
for i in range(n - k + 1, n + 1):
p = (p * i) % mod
for i in range(2, k + 1):
q = (q * i) % mod
return p * (xgcd(q, mod)[0] % mod) % mod
X, Y = list(map(int, input().split()))
b = (2 * X - Y) // 3
a = (-X + 2 * Y) // 3
if (X + Y) % 3 != 0 or a < 0 or b < 0:
print((0))
else:
print((nCk(a + b, a)))
main()
| def nCk(n, k, mod=10 ** 9 + 7):
if n < k:
return 0
k = min(k, n - k)
numer = 1
for x in range(n - k + 1, n + 1):
numer = (numer * x) % mod
denom = 1
for x in range(1, k + 1):
denom = (denom * x) % mod
return numer * pow(denom, mod - 2, mod) % mod
X, Y = list(map(int, input().split()))
b = (2 * X - Y) // 3
a = (-X + 2 * Y) // 3
if (X + Y) % 3 != 0 or a < 0 or b < 0:
print((0))
else:
print((nCk(a + b, a))) | p02862 |
def comb_mod(n,r,m):
ans = 1
for i in range(1,r+1):
ans *= (n-i+1) % m
ans *= pow(i,m-2,m) % m
ans = ans % m
return ans
x,y = list(map(int,input().split()))
m = 10**9+7
n = (x+y)//3
c = 0
if x*0.5 <= y <= 2*x and (x+y)%3 == 0:
r = x - n
c = comb_mod(n,r,m)
else:
ans = 0
print(c)
| def comb_mod(n,r,m):
ans = 1
for i in range(1,r+1):
ans *= (n-i+1) % m
ans *= pow(i,m-2,m) % m
ans = ans % m
return ans
x,y = list(map(int,input().split()))
m = 10**9+7
if x > 2*y or 2*x < y or (x+y)%3 != 0:
ans = 0
else:
n = (x+y)//3
r = x-n
ans = comb_mod(n,r,m)
print(ans) | p02862 |
M=10**9+7
x,y=list(map(int,input().split()))
ans=0
if (x+y)%3==0:
a=(2*y-x)//3
b=(2*x-y)//3
if a>=0 and b>=0:
f1,f2=1,1
for i in range(a+1,a+b+1):
f1*=i
f1%=M
for i in range(1,b+1):
f2*=i
f2%=M
ans=f1*pow(f2,M-2,M)
print((ans%M)) | X,Y=list(map(int,input().split()))
if 2*Y<X or 2*X<Y:
print((0))
exit()
if not((X%3==0 and Y%3==0) or (X%3==1 and Y%3==2) or (X%3==2 and Y%3==1)):
print((0))
exit()
P=10**9+7
A=(2*Y-X)//3
B=(2*X-Y)//3
num = 1
for i in range(A+1, A+B+1):
num=num*i%P
den = 1
for j in range(1, B+1):
den = den*j%P
den = pow(den,P-2,P)
print(((num*den)%P)) | p02862 |
mod = 10**9 + 7
def nCk(n,k,p):
global mod
k = min(k, n-k)
X = 1
for i in range(k):
X = X * (n - i) % p
X = X * pow(i + 1, p - 2, p) % p
return X
X,Y = list(map(int, input().split()))
ans = 0
if X <= 2*Y and Y <= 2*X and (X + Y) % 3 == 0:
a = (2*Y-X) // 3
b = (2*X-Y) // 3
ans = nCk(a + b, b, mod)
print(ans) | X,Y = list(map(int, input().split()))
mod = 10**9 + 7
def nCk(n,k,p):
fact = [1,1] + [0]*(n-1)
inv = [0,1] + [0]*(n-1)
factinv = [1,1] + [0]*(n-1)
for i in range(2, n+1):
fact[i] = i * fact[i-1] % p
inv[i] = - inv[p % i] * (p // i) % p
factinv[i] = factinv[i-1] * inv[i] % p
return fact[n] * factinv[k] * factinv[n-k] % p
ans = 0
if (X + Y) % 3 == 0 and X <= 2*Y and Y <= 2*X:
a = (2*Y - X) // 3
b = (2*X - Y) // 3
ans = nCk(a+b, a, mod)
print(ans) | p02862 |
def comb(n, r, p):
x, y = 1, 1
for i in range(n, n - r, -1):
x *= i
y *= i + r - n
x %= p
y %= p
return pow(y, p - 2, p) * x % p
x, y = list(map(int, input().split()))
n = (x + y) // 3
p = 10 ** 9 + 7
if (x + y) % 3 == 0:
r = 0
if x > y:
x, y = y, x
while True:
if 2 * x == y:
break
r += 1
x -= 2
y -= 1
print((comb(n, r, p)))
else:
print((0)) | def comb(n, r, p):
x, y = 1, 1
for i in range(n, n - r, -1):
x *= i
y *= i + r - n
x %= p
y %= p
return pow(y, p - 2, p) * x % p
x, y = list(map(int, input().split()))
n = (x + y) // 3
p = 10 ** 9 + 7
if (x + y) % 3 == 0 and max(x, y) <= 2 * min(x, y):
r = 0
if x > y:
x, y = y, x
a = (2 * x - y) // 3
r = min(a, n - a)
print((comb(n, r, p)))
else:
print((0)) | p02862 |
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
mod = 10**9+7
def comb(n, k):
c = 1
for i in range(k):
c *= n - i
c %= mod
d = 1
for i in range(1, k + 1):
d *= i
d %= mod
return (c * pow(d, mod - 2, mod)) % mod
x,y = list(map(int, input().split()))
if (x + y) % 3 != 0:
print((0))
exit()
n = (x + y) // 3
x -= n
y -= n
if x < 0 or y < 0:
print((0))
exit()
print((comb(x + y, x)))
| import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
mod = 10**9+7
def comb(n, k):
c = 1
for i in range(k):
c *= n - i
c %= mod
d = 1
for i in range(1, k + 1):
d *= i
d %= mod
return (c * pow(d, mod - 2, mod)) % mod
x,y = list(map(int, input().split()))
if (x + y) % 3 != 0:
print((0))
exit()
# 公式解説解答
# n = (x + y) // 3
# x -= n
# y -= n
# if x < 0 or y < 0:
# print(0)
# exit()
# print(comb(x + y, x))
# x = 2a + b
# y = a + 2b
# 連立方程式を解いてa,bを求める
# あとはa,bの同じものを含む順列(a+b)!/a!b!
a = (2 * x - y) // 3
b = (-x + 2 * y) // 3
if a < 0 or b < 0:
print((0))
exit()
print((comb((x + y) // 3, a)))
| p02862 |
def comb(n, k, mod):
if k > (n // 2):
k = n - k
a = 1
for i in range(k):
a *= (n - i)
a %= mod
for i in range(k - 1):
a = (a * pow(k - i, mod - 2, mod)) % mod
return a
X, Y = list(map(int, input().split()))
ans = 0
mod = 10 ** 9 + 7
if X > Y:
X, Y = Y, X
##Yのほうが大きいとして考える
if not (X + Y) % 3 == 0 or Y > 2 * X:
ans = 0
else:
n = (X + Y) // 3
d = Y - X
a = 2*n - X
ans = comb(n, a, mod)
print(ans)
| def comb(n, k, mod):
if k > (n // 2):
k = n - k
a = 1
for i in range(k):
a = (a * (n - i)) % mod
b = 1
for i in range(k - 1):
b = (b *(k - i)) % mod
a = (a * pow(b, mod - 2, mod)) % mod
return a
X, Y = list(map(int, input().split()))
ans = 0
mod = 10 ** 9 + 7
if X > Y:
X, Y = Y, X
##Yのほうが大きいとして考える
if not (X + Y) % 3 == 0 or Y > 2 * X:
ans = 0
else:
n = (X + Y) // 3
d = Y - X
a = 2*n - X
ans = comb(n, a, mod)
print(ans)
| p02862 |
X,Y=list(map(int,input().split()))
mod=10**9+7
if (X+Y)%3!=0:
print((0));exit()
if X*2<Y or Y*2<X:
print((0));exit()
t=(X+Y)//3
f=[1]
for i in range(1,t+100):
f.append(f[-1]*i%mod)
def comb(a,b,m):
return f[a]*pow(f[b],m-2,m)*pow(f[a-b],m-2,m)%m
print((comb(t,X-t,mod)))
| M=10**9+7
x,y=list(map(int,input().split()))
ans=0
if (x+y)%3==0:
a=(2*y-x)//3
b=(2*x-y)//3
if a>=0 and b>=0:
f1,f2=1,1
for i in range(a+1,a+b+1):
f1*=i
f1%=M
for i in range(1,b+1):
f2*=i
f2%=M
ans=f1*pow(f2,M-2,M)
print((ans%M))
| p02862 |
fac = [0] * 700000
finv = [0] * 700000
inv = [0] * 700000
mod = 1000000007
fac[0] = fac[1] = 1
finv[0] = finv[1] = 1
inv[1] = 1
for i in range(2, 700000):
fac[i] = fac[i - 1] * i % mod
inv[i] = mod - inv[mod % i] * (mod // i) % mod
finv[i] = finv[i - 1] * inv[i] % mod
x, y = list(map(int, input().split()))
if (x + y) % 3 == 0:
k = (2 * x - y) // 3
l = (2 * y - x) // 3
if k >= 0 and l >= 0:
print((fac[k + l] * (finv[k] * finv[l] % mod) % mod))
else:
print((0))
else:
print((0))
| mod = 10 ** 9 + 7
ans = 0
x, y = list(map(int, input().split()))
if (x + y) % 3 == 0:
k = (2 * x - y) // 3
l = (2 * y - x) // 3
if k >= 0 and l >= 0:
fac = [1] * (k + l + 1)
for i in range(2, k + l + 1):
fac[i] = fac[i - 1] * i % mod
ans = fac[k + l] * (pow(fac[k], mod - 2, mod) * pow(fac[l], mod - 2, mod) % mod) % mod
print(ans)
| p02862 |
x,y = list(map(int,input().split()))
ans = 0
mod = 10**9+7
if (x+y)%3 == 0:
m = (2*y-x)//3
n = (2*x-y)//3
if m >= 0 and n >= 0:
fac = [1]*(m+n+1)
for i in range(2,m+n+1):
fac[i] = fac[i-1]*i % mod
ans = fac[m+n]*(pow(fac[m],mod-2,mod)*pow(fac[n],mod-2,mod)%mod)%mod
print(ans) | def comb(n,k,mod):
x = y = 1
for i in range(min(k,n-k)):
x = x*(n-i)%mod
y = y*(i+1)%mod
return x * pow(y, mod-2, mod) % mod
x,y = list(map(int,input().split()))
ans = 0
mod = 10**9+7
if (x+y)%3 == 0:
a = (-x+2*y)//3
b = (2*x-y)//3
if a >= 0 and b >= 0: ans = comb(a+b,a,mod)
print(ans) | p02862 |
def cmb(n, r, mod):
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 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 = list(map(int,input().split()))
a = ( 2 * x - y )
b = ( - x + 2 * y )
if a % 3 != 0 or b % 3 != 0:
print((0))
exit(0)
a = int(a/3)
b = int(b/3)
# print(a, b)
mod = 10**9 + 7
ans = cmb((a+b),a,mod)
print(ans) | def cmb(n, r, mod):
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 #出力の制限
N = 10**6
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
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 = list(map(int,input().split()))
a = 2 * x - y
b = - x + 2 * y
ans = 0
if a % 3 == 0 and b % 3 == 0:
a = a//3
b = b//3
ans = cmb(a+b, a, mod)
print(ans) | p02862 |
x,y = list(map(int,input().split()))
class ModComb:
def __init__(self, MAX, mod=10 ** 9 + 7):
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]
for i in range(2, MAX):
fac.append(fac[i - 1] * i % mod)
inv.append(mod - inv[mod % i] * (mod // i) % mod)
finv.append(finv[i - 1] * inv[i] % mod)
self.fac, self.finv, self.mod = fac, finv, mod
def nCk(self, n, k):
if n < k or n < 0 or k < 0:
return 0
fac, finv, mod = self.fac, self.finv, self.mod
return fac[n] * (finv[k] * finv[n - k] % mod) % mod
if (x+y)%3!=0:
print((0))
else:
a = (2*x - y) // 3
b = (2*y - x) // 3
mod = 10 ** 9 + 7
mc = ModComb(1000000, mod=mod)
print((mc.nCk(a + b, a) % mod)) | X,Y = list(map(int,input().split()))
n = (-X+2*Y)//3
m = (2*X-Y)//3
mod = 10**9+7 #出力の制限
N = max(n+m,n)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % 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 )
if (-X+2*Y)%3 == 0 and (2*X-Y)%3 == 0:
print((cmb(n+m,n,mod)))
else:
print((0)) | p02862 |
X,Y = list(map(int,input().split()))
n = (-X+2*Y)//3
m = (2*X-Y)//3
mod = 10**9+7 #出力の制限
N = max(n+m,n)
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % 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 )
if (-X+2*Y)%3 == 0 and (2*X-Y)%3 == 0:
print((cmb(n+m,n,mod)))
else:
print((0)) | X,Y = list(map(int,input().split()))
n = (-X+2*Y)//3
m = (2*X-Y)//3
MOD = 10**9+7
def comb(n,r,MOD):
x = n+1
y = min(r,n-r)
numer = 1
denom = 1
for i in range(1,r+1):
numer = numer*(x-i)%MOD
denom = denom*(i)%MOD
return numer * pow(denom,MOD-2,MOD) % MOD
import sys
if n < 0 or m < 0:
print((0))
sys.exit()
if (X+Y)%3 != 0:
print((0))
sys.exit()
print((comb(n+m,n,MOD))) | p02862 |
def cmb(n, r, mod):
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
nums = 10**6 # 制約に合わせよう
g1, g2, inverse = [1, 1] , [1, 1], [0, 1]
for num in range(2, nums + 1):
g1.append((g1[-1] * num) % mod)
inverse.append((-inverse[mod % num] * (mod//num)) % mod)
g2.append((g2[-1] * inverse[-1]) % mod)
x, y = list(map(int, input().split()))
if (x+y)%3 or 2*x<y or 2*y<x:
print((0))
else:
print((cmb((x+y)//3,(2*x-y)//3, mod))) | def nCr(n, r, mod):
x, y = 1, 1
for r_ in range(1, r+1):
x = x*(n+1-r_)%mod
y = y*r_%mod
return x*pow(y, mod-2, mod)%mod
x, y = list(map(int, input().split()))
mod = 10**9+7
if (x+y)%3 or 2*x<y or 2*y<x:
print((0))
else:
print((nCr((x+y)//3,(2*x-y)//3, mod))) | p02862 |
MAX = 1000010
finv = [0] * MAX
inv = [0] * MAX
def COMinit():
finv[0] = finv[1] = 1
inv[1] = 1
for i in range(2, MAX):
inv[i] = MOD - inv[MOD%i] * (MOD//i) % MOD
finv[i] = finv[i-1] * inv[i] % MOD
def COM(n, k):
res = 1
for i in range(k):
res = res * (n-i) % MOD
return res * finv[k] % MOD
MOD = 10**9+7
x, y = list(map(int, input().split()))
s, t = (-x+2*y)/3, (2*x-y)/3
if s < 0 or t < 0:
ans = 0
elif not (s.is_integer() and t.is_integer()):
ans = 0
else:
s, t = int(s), int(t)
COMinit()
ans = COM((s+t), s)
print(ans) | MOD = 10**9+7
MAX = 1000010
finv = [0] * MAX
inv = [0] * MAX
def COMinit():
finv[0] = finv[1] = 1
inv[1] = 1
for i in range(2, MAX):
inv[i] = MOD - inv[MOD%i] * (MOD//i) % MOD
finv[i] = finv[i-1] * inv[i] % MOD
def COM(n, k):
res = 1
for i in range(k):
res = res * (n-i) % MOD
return res * finv[k] % MOD
x, y = list(map(int, input().split()))
if (x+y)%3 != 0:
ans = 0
else:
s, t = (-x+2*y)//3, (2*x-y)//3
if s < 0 or t < 0:
ans = 0
else:
COMinit()
ans = COM((s+t), s)
print(ans) | p02862 |
MOD = 10**9+7
X, Y = sorted(list(map(int, input().split())))
if (X+Y)%3 != 0:
print((0))
exit()
if (2*X < Y):
print((0))
exit()
W = X - ((X+Y)//3)
H = Y - ((X+Y)//3)
mx = 10**6
fact = [1] * (mx+1) # 階乗を格納するリスト
def inv(n): # MODを法とした逆元
return pow(n, MOD-2, MOD)
for i in range(mx):
fact[i+1] = fact[i] * (i+1) % MOD # 階乗を計算
ans = (fact[W+H] * inv(fact[W]) * inv(fact[H])) % MOD # comb(W+H,W) = (W+H)!/(W!H!)
print (ans) | MOD = 10**9+7
X, Y = list(map(int, input().split()))
if (X > Y):
X, Y = Y, X
if (X+Y)%3 != 0:
print((0))
exit()
if (2*X < Y):
print((0))
exit()
W = X - ((X+Y)//3)
H = Y - ((X+Y)//3)
mx = 10**6
fact = [1] * (mx+1) # 階乗を格納するリスト
def inv(n): # MODを法とした逆元
return pow(n, MOD-2, MOD)
for i in range(mx):
fact[i+1] = fact[i] * (i+1) % MOD # 階乗を計算
ans = (fact[W+H] * inv(fact[W]) * inv(fact[H])) % MOD # comb(W+H,W) = (W+H)!/(W!H!)
print (ans) | p02862 |
def num_combinations_mod(n, r, mod, num_max=10**6):
# if this functions is called twice or more, init process should be placed before calling this function to
# save time.
if r > n:
return 0
elif r == n:
return 1
elif r < 0 or n < 0:
return 0
f_mod, f_mod_inv = num_combinations_mod_init(num_max, mod)
return f_mod[n] * (f_mod_inv[r] * f_mod_inv[n-r] % mod) % mod
def num_combinations_mod_init(num_max, mod):
factorials_mod = dict()
factorials_mod_inv = dict()
factorials_mod[0] = 1
factorials_mod[1] = 1
factorials_mod_inv[0] = 1
factorials_mod_inv[1] = 1
mod_inv = dict()
mod_inv[1] = 1
for i in range(2, num_max):
factorials_mod[i] = factorials_mod[i - 1] * i % mod
mod_inv[i] = mod - mod_inv[mod % i] * (mod // i) % mod
factorials_mod_inv[i] = factorials_mod_inv[i - 1] * mod_inv[i] % mod
return factorials_mod, factorials_mod_inv
def get(num1, num2):
if num1 > num2:
num = num2
else:
num = num1
return num_combinations_mod(num1+num2, num, 10**9+7)
def main(X, Y):
if (X + Y) % 3 != 0:
return 0
total = (X + Y) // 3
n_moveB = (2 * X - Y) // 3
n_moveA = total - n_moveB
answer = get(n_moveA, n_moveB)
return answer
X, Y = list(map(int, input().split(" ")))
print((main(X, Y))) | def num_combinations_mod2(n, r, mod=10 ** 9 + 7):
# mod must be a prime.
# nCr = (n! / (n-r)!) * (r!)^-1
# a = n! / (n-r)!
# b = (r!)^-1
if r > n:
return 0
if r < 0 or n < 0:
return 0
r = min(r, n - r)
a = 1
b = 1
for i in range(1, r + 1):
a = a * (n + 1 - i) % mod
b = b * i % mod
return a * pow(b, mod - 2, mod) % mod
def main(x, y):
if (x + y) % 3 != 0:
return 0
total = (x + y) // 3
n = (2 * x - y) // 3
m = total - n
answer = num_combinations_mod2(m+n, n, 10**9+7)
return answer
X, Y = list(map(int, input().split(" ")))
print((main(X, Y)))
| p02862 |
def nCr(n,r):
dividend,divisor = 1,1
for i in range(r):
dividend *= n-i
divisor *= 1+i
dividend %= MOD
divisor %= MOD
return (dividend * pow(divisor, MOD-2, MOD)) % MOD
X,Y = list(map(int,input().split()))
INF = 10**15
MOD = 10**9+7
if (X+Y)%3!=0:
print((0))
exit()
n = (-X + 2*Y) // 3
m = (2*X - Y) // 3
if n<0 or m<0:
print((0))
exit()
print((nCr(n+m, n))) | def nCr(n,r):
dividend = 1
divisor = 1
MOD = 10**9+7
d1 = n
for i in range(1,r+1):
dividend *= d1
divisor *= i
d1 -= 1
dividend %= MOD
divisor %= MOD
return (dividend * pow(divisor, MOD-2, MOD)) % MOD
X,Y = list(map(int,input().split()))
if (X+Y) % 3 != 0:
print((0))
exit()
n = (-X+2*Y) // 3
m = (2*X-Y) // 3
if n<0 or m<0:
print((0))
else:
print((nCr(n+m, n))) | p02862 |
MOD = 10 ** 9 + 7
def prepare(n):
global MOD
modFacts = [0] * (n + 1)
modFacts[0] = 1
for i in range(n):
modFacts[i + 1] = (modFacts[i] * (i + 1)) % MOD
invs = [1] * (n + 1)
invs[n] = pow(modFacts[n], MOD - 2, MOD)
for i in range(n, 1, -1):
invs[i - 1] = (invs[i] * i) % MOD
return modFacts, invs
dest = list(map(int, input().split()))
p = (2, 1)
q = (1, 2)
num_p = 0
num_q = 0
while dest[0] and dest[1]:
if dest[0] >= dest[1]:
dest[0] -= p[0]
dest[1] -= p[1]
num_p += 1
else:
dest[0] -= q[0]
dest[1] -= q[1]
num_q += 1
modFacts, invs = prepare(num_p + num_q)
if dest == [0, 0]:
n = num_p + num_q
r = min(num_p, num_q)
ans = (modFacts[n] * invs[n - r] * invs[r]) % MOD
else:
ans = 0
print(ans)
| MOD = 10 ** 9 + 7
def prepare(n):
global MOD
modFacts = [0] * (n + 1)
modFacts[0] = 1
for i in range(n):
modFacts[i + 1] = (modFacts[i] * (i + 1)) % MOD
invs = [1] * (n + 1)
invs[n] = pow(modFacts[n], MOD - 2, MOD)
for i in range(n, 1, -1):
invs[i - 1] = (invs[i] * i) % MOD
return modFacts, invs
X, Y = list(map(int, input().split()))
if (X + Y) % 3 == 0 and 2 * Y - X >= 0 and 2 * X - Y >= 0:
p = (2 * Y - X) // 3
q = (2 * X - Y) // 3
n = p + q
r = min(p, q)
modFacts, invs = prepare(n)
ans = (modFacts[n] * invs[n - r] * invs[r]) % MOD
else:
ans = 0
print(ans)
| p02862 |
#べき乗関数powを使った逆元の計算
def modinv2(a,m):
return pow(a,m-2,m)
X,Y = list(map(int,input().split()))
X,Y = min(X,Y),max(X,Y)
if (X+Y)%3 != 0 or X*2-Y < 0:
ans = 0
else:
a = (2*X-Y)//3
b = (2*Y-X)//3
m = 10**9+7
ans = 1
for i in range(1,a+b+1):
ans = ans*i%m
for i in range(1,a+1):
ans = ans*modinv2(i,m)%m
for i in range(1,b+1):
ans = ans*modinv2(i,m)%m
print(ans)
| #べき乗関数powを使った逆元の計算
def modinv2(a,m):
return pow(a,m-2,m)
X,Y = list(map(int,input().split()))
X,Y = min(X,Y),max(X,Y)
if (X+Y)%3 != 0 or X*2-Y < 0:
ans = 0
else:
a = (2*X-Y)//3
b = (2*Y-X)//3
m = 10**9+7
ans = 1
for i in range(b+1,a+b+1):
ans = ans*i%m
for i in range(1,a+1):
ans = ans*modinv2(i,m)%m
print(ans)
| p02862 |
#拡張ユークリッド互除法
#ax+by=1の1つの解(gcd(a,b)=1)
def extgcd(a,b):
r = [1,0,a]
w = [0,1,b]
while w[2] != 1:
q = r[2]//w[2]
r2 = w
w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
r = r2
w = w2
#[x,y]
return [w[0],w[1]]
# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def modinv(a,m):
x = extgcd(a,m)[0]
return (m+x%m)%m #負の値を返さないように
X,Y = list(map(int,input().split()))
X,Y = min(X,Y),max(X,Y)
if (X+Y)%3 != 0 or X*2-Y < 0:
ans = 0
else:
a = (2*X-Y)//3
b = (2*Y-X)//3
m = 10**9+7
ans = 1
for i in range(b+1,a+b+1):
ans = ans*i%m
for i in range(1,a+1):
ans = ans*modinv(i,m)%m
print(ans)
| #拡張ユークリッド互除法
#ax+by=1の1つの解(gcd(a,b)=1)
#仕組みをちゃんと理解していない
def extgcd(a,b):
r = [1,0,a]
w = [0,1,b]
while w[2] != 1:
q = r[2]//w[2]
r2 = w
w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
r = r2
w = w2
#[x,y]
return [w[0],w[1]]
# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def modinv(a,m):
x = extgcd(a,m)[0]
return (m+x%m)%m #負の値を返さないように
X,Y = list(map(int,input().split()))
X,Y = min(X,Y),max(X,Y)
if (X+Y)%3 != 0 or X*2-Y < 0:
ans = 0
else:
a = (2*X-Y)//3
b = (2*Y-X)//3
m = 10**9+7
ans = 1
for i in range(b+1,a+b+1):
ans = ans*i%m
for i in range(1,a+1):
ans = ans*modinv(i,m)%m
print(ans)
| p02862 |
def modinv(a,m):
return pow(a,m-2,m)
x,y = list(map(int,input().split()))
if (x+y)%3 != 0 or 2*y-x < 0 or 2*x-y < 0:
print((0))
else:
a = (2*y-x)//3
b = (2*x-y)//3
ans = 1
mod = 10**9+7
for i in range(1,a+1):
ans = ans*(i+b)*modinv(i,mod)%mod
print(ans)
| #nCrをmodで割った余りO(r)
def comb(n, r, mod):
r = min(r, n-r)
mol = 1
deno = 1
for i in range(1, r+1):
mol = mol * (n-r+i) % mod
deno = deno * i % mod
ret = mol * pow(deno, mod-2, mod) % mod
return ret
x,y = list(map(int,input().split()))
if (x+y)%3 != 0 or 2*y-x < 0 or 2*x-y < 0:
print((0))
else:
a = (2*y-x)//3
b = (2*x-y)//3
mod = 10**9+7
print((comb(a+b,a,mod)))
| p02862 |
def p_d():
x, y = list(map(int, input().split()))
if y > x:
x, y = y, x
if (x + y) % 3 != 0:
print((0))
exit()
if x - y > (x + y) // 3:
print((0))
exit()
x, y = x - (x + y) // 3, y - (x + y) // 3
mod = 10 ** 9 + 7 # 出力の制限
N = x + y
g1 = [1, 1] # 元テーブル
g2 = [1, 1] # 逆元テーブル
inverse = [0, 1] # 逆元テーブル計算用テーブル
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)
def cmb(n, r, mod):
if (r < 0 or r > n):
return 0
r = min(r, n - r)
return g1[n] * g2[r] * g2[n - r] % mod
print((cmb(x + y, y, mod)))
p_d() | def p_d():
x, y = list(map(int, input().split()))
if y > x:
x, y = y, x
if (x + y) % 3 != 0:
print((0))
exit()
if x - y > (x + y) // 3:
print((0))
exit()
x, y = x - (x + y) // 3, y - (x + y) // 3
def c_mod(n, r, mod=10 ** 9 + 7):
n1, r = n + 1, min(r, n - r)
numer = denom = 1
for i in range(1, r + 1):
numer = numer * (n1 - i) % mod
denom = denom * i % mod
return numer * pow(denom, mod - 2, mod) % mod
print((c_mod(x + y, y)))
p_d() | p02862 |
X,Y = list(map(int,input().split()))
if X>Y:
X,Y = Y,X
if(X+Y)%3:
print((0))
exit()
n = (X+Y)//3
if X < n:
print((0))
exit()
MOD = 10**9+7
r = X-n
maxn = n+5
fac = [1,1] + [0]*maxn
finv = [1,1] + [0]*maxn
inv = [0,1] + [0]*maxn
for i in range(2,maxn+2):
fac[i] = fac[i-1] * i % MOD
inv[i] = -inv[MOD%i] * (MOD // i) % MOD
finv[i] = finv[i-1] * inv[i] % MOD
def ncr(n,r):
if n < r: return 0
if n < 0 or r < 0: return 0
return fac[n] * (finv[r] * finv[n-r] % MOD) % MOD
print((ncr(n,r))) | X,Y = list(map(int,input().split()))
MOD = 10**9+7
if (X+Y)%3:
print((0))
exit()
n = (X+Y)//3
r = X-n
if not 0 <= r <= n:
print((0))
exit()
MAXN = r
inv = [0,1] + [0]*MAXN
for i in range(2,MAXN+2):
inv[i] = -inv[MOD%i] * (MOD // i) % MOD
def comb(n,r):
ret = 1
for i in range(r):
ret *= n-i
ret *= inv[i+1]
ret %= MOD
return ret
print((comb(n,r))) | p02862 |
def sq(a, b, mod): # aのb乗を剰余,kは初期値#20191116-D-Knight
if b == 0:
return 1
elif b % 2 == 0:
return sq(a, b // 2, mod)**2 % mod
else:
return sq(a, b - 1, mod) * a % mod
def nCk(n, k, mod=10**9 + 7):
x = max(k, n - k)
y = min(k, n - k)
kkai = 1
for i in range(2, y + 1):
kkai = (kkai * i) % mod
nkkai = 1
for i in range(x + 1, n + 1):
nkkai = (nkkai * i) % mod
answer = sq(kkai, mod - 2, mod) * nkkai % mod
return answer
from sys import exit
X, Y = list(map(int, input().split()))
if (X + Y) % 3 != 0:
print((0))
exit()
if X % 2 == 0:
syurui = X - (X // 2) + 1
else:
syurui = X - (X // 2)
for i in range(syurui):
two = i
one = X - two * 2
if (two + one * 2) == Y:
print((nCk(two + one, two)))
exit()
print((0))
| def sq(a, b, mod): # aのb乗を剰余,kは初期値#20191116-D-Knight
if b == 0:
return 1
elif b % 2 == 0:
return sq(a, b // 2, mod)**2 % mod
else:
return sq(a, b - 1, mod) * a % mod
def nCk(n, k, mod=10 ** 9 + 7):
x = max(k, n - k)
y = min(k, n - k)
kkai = 1
for i in range(2, y + 1):
kkai = (kkai * i) % mod
nkkai = 1
for i in range(x + 1, n + 1):
nkkai = (nkkai * i) % mod
answer = sq(kkai, mod - 2, mod) * nkkai % mod
return answer
X, Y = list(map(int, input().split()))
if (X + Y) % 3 != 0:
print((0))
else:
n = (2 * Y - X) // 3
m = (2 * X - Y) // 3
if n < 0 or m < 0:
print((0))
else:
print((nCk(n + m, n)))
| p02862 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.