提出 #8515308

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ソースコード 拡げる

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

import numpy as np

MOD = 10 ** 9 + 7

N = int(readline())
m = map(int,read().split())
AB = zip(m,m)

D = 2000

U = 10 ** 4
fact = [1] * U
for n in range(1,U):
    fact[n] = fact[n-1] * n % MOD
fact_inv = [1] * U
fact_inv[-1] = pow(fact[-1],MOD-2,MOD)
for n in range(U-1,0,-1):
    fact_inv[n-1] = fact_inv[n] * n % MOD

C_to_A = [[] for _ in range(D+D+1)]
Y = 0
for a,b in AB:
    c = a+b
    C_to_A[c].append(D-a)
    Y += fact[c+c] * fact_inv[a+a] * fact_inv[b+b]
Y %= MOD

f = np.zeros(D+D+1,np.int64)
for A in C_to_A[::-1]:
    f[1:] += f[:-1].copy()
    np.add.at(f,A,1)
    f %= MOD
X = (f * f[::-1] % MOD).sum() % MOD

answer = (X - Y) * fact_inv[2] % MOD
print(answer)

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