結果

問題 No.2499 Sum of Products of Sums
ユーザー KumaTachiRen
提出日時 2023-09-18 17:14:14
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 494 ms / 2,000 ms
コード長 2,401 bytes
コンパイル時間 147 ms
コンパイル使用メモリ 82,436 KB
実行使用メモリ 78,948 KB
最終ジャッジ日時 2024-07-05 07:23:07
合計ジャッジ時間 4,461 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 17
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ソースコード

diff #
プレゼンテーションモードにする

MOD = 998244353
K, M, W = 119, 23, 31
# https://qiita.com/izu_nori/items/1c5cdef0500ffa0276f5
class NTT:
    def __init__(self):
        self.ws = [pow(W, 2**i, MOD) for i in range(M, -1, -1)]
        self.iws = [pow(w, MOD - 2, MOD) for w in self.ws]
    def convolution(self, f, g):
        nf = len(f)
        ng = len(g)
        m = nf + ng - 1
        n = 2 ** (m - 1).bit_length()
        f = [x % MOD for x in f] + [0] * (n - nf)
        g = [x % MOD for x in g] + [0] * (n - ng)
        self.ntt(f)
        self.ntt(g)
        for i in range(n):
            f[i] = f[i] * g[i] % MOD
        self.intt(f)
        return f[:m]
    def ntt(self, A):
        if len(A) == 1:
            return
        n = len(A)
        k = n.bit_length() - 1
        r = 1 << (k - 1)
        for w in self.ws[k:0:-1]:
            for l in range(0, n, 2 * r):
                wi = 1
                for i in range(r):
                    A[l + i], A[l + i + r] = (A[l + i] + A[l + i + r]) % MOD, (A[l + i] - A[l + i + r]) * wi % MOD
                    wi = wi * w % MOD
            r = r // 2
    def intt(self, A):
        if len(A) == 1:
            return
        n = len(A)
        k = (n - 1).bit_length()
        r = 1
        for w in self.iws[1 : k + 1]:
            for l in range(0, n, 2 * r):
                wi = 1
                for i in range(r):
                    A[l + i], A[l + i + r] = (A[l + i] + A[l + i + r] * wi) % MOD, (A[l + i] - A[l + i + r] * wi) % MOD
                    wi = wi * w % MOD
            r = r * 2
        ni = pow(n, MOD - 2, MOD)
        for i in range(n):
            A[i] = A[i] * ni % MOD
FACT_SIZE = 3000
fact = [1] * FACT_SIZE
for i in range(1, FACT_SIZE):
    fact[i] = fact[i - 1] * i % MOD
ifact = [1] * FACT_SIZE
ifact[FACT_SIZE - 1] = pow(fact[FACT_SIZE - 1], MOD - 2, MOD)
for i in range(FACT_SIZE - 1, 0, -1):
    ifact[i - 1] = ifact[i] * i % MOD
h, w = map(int, input().split(" "))
f = [fact[w]]
ntt = NTT()
for _ in range(h):
    a, b = map(int, input().split(" "))
    a -= 1
    g = [0] * (w + 1)
    ff_a, ff_b = 1, 1
    for n in range(w):
        ff_a = ff_a * (w + a - n) % MOD
        ff_b = ff_b * (w + b - n) % MOD
    for n in range(w + 1):
        g[n] = ifact[n] * ifact[w + n] % MOD * (ff_b - ff_a) % MOD
        ff_a = ff_a * (a - n) % MOD
        ff_b = ff_b * (b - n) % MOD
    f = ntt.convolution(f, g)[: w + 1]
print(f[w])
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