Submission #7963341

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Source Code Expand

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

import numpy as np

MOD = 998244353

"""
・(xyz+1/(xyz)+x+1/x+y+1/y+z+1/z) = (1/xyz)(xy+1)(yz+1)(xz+1) これのn乗して、mod m で(p,q,r)の係数
・xyの係数をkとすると、xz,yzの係数 mod k が決まる
・(T+1)^nをmod mでまとめておけばよい
"""

N,M,P,Q,R = map(int,read().split())

def cumprod(arr,MOD):
    L = len(arr); Lsq = int(L**.5+1)
    arr = np.resize(arr,Lsq**2).reshape(Lsq,Lsq)
    for n in range(1,Lsq):
        arr[:,n] *= arr[:,n-1]; arr[:,n] %= MOD
    for n in range(1,Lsq):
        arr[n] *= arr[n-1,-1]; arr[n] %= MOD
    return arr.ravel()[:L]

def make_fact(U,MOD):
    x = np.arange(U,dtype=np.int64); x[0] = 1
    fact = cumprod(x,MOD)
    x = np.arange(U,0,-1,dtype=np.int64); x[0] = pow(int(fact[-1]),MOD-2,MOD)
    fact_inv = cumprod(x,MOD)[::-1]
    return fact,fact_inv

U = N+100
fact,fact_inv = make_fact(U,MOD)
# (1+T)^N
F = fact[N] * fact_inv[:N+1] % MOD * fact_inv[N::-1] % MOD

# i+j = n+r, i+k = n+q, j+k = n+p mod M
# 2i = (n+r)+(n+q)-(n+p) = n+q+r-p mod M

x = (N+Q+R-P) % M
if M&1:
    if x&1: x += M
    I = [x//2]
else:
    if x&1:
        I = []
    else:
        I = [x//2,(x+M)//2]

answer = 0
for i in I:
    j = (N+R-i)%M
    k = (N+Q-i)%M
    a = F[i::M].sum() % MOD
    b = F[j::M].sum() % MOD
    c = F[k::M].sum() % MOD
    answer += a * b % MOD * c % MOD
answer %= MOD
print(answer)

Submission Info

Judge Result