#851091 (PyPy3) No.1973 Divisor Sequence

• 問題: No.1973 Divisor Sequence
• ユーザー: mkawa2
• 提出日時: 2023-03-19 00:09:37
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 91 ms / 2,000 ms
• コード長: 2,104 bytes
• コンパイル時間: 293 ms
• コンパイル使用メモリ: 82,184 KB
• 実行使用メモリ: 76,160 KB
• 最終ジャッジ日時: 2024-09-18 13:38:06
• 合計ジャッジ時間: 2,107 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 22

ソースコード

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import sys
# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
md = 10**9+7
# md = 998244353
# 行列累乗バージョン
def prime_factorization(a):
    pp, ee = [], []
    if a & 1 == 0:
        pp += [2]
        ee += [0]
        while a & 1 == 0:
            a >>= 1
            ee[-1] += 1
    p = 3
    while p**2 <= a:
        if a%p == 0:
            pp += [p]
            ee += [0]
            while a%p == 0:
                a //= p
                ee[-1] += 1
        p += 2
    if a > 1:
        pp += [a]
        ee += [1]
    return pp, ee
def dot(aa, bb):
    h = len(aa)
    w = len(bb[0])
    res = [[0]*w for _ in range(h)]
    for j, col in enumerate(zip(*bb)):
        for i in range(h):
            v = 0
            # for a, b in zip(row, col): v += a*b
            # res[i][j] = v
            for a, b in zip(aa[i], col): v += a*b%md
            res[i][j] = v%md
    return res
def matpow(mat, e):
    n = len(mat)
    res = [[1 if i == j else 0 for j in range(n)] for i in range(n)]
    while e:
        if e & 1: res = dot(res, mat)
        mat = dot(mat, mat)
        e >>= 1
    return res
n, m = LI()
ans = 1
_, ee = prime_factorization(m)
for e in ee:
    mat = [[0]*(e+1) for _ in range(e+1)]
    for i in range(e+1):
        for j in range(e+1):
            if i+j <= e: mat[i][j] = 1
    mat = matpow(mat, n-1)
    s = 0
    for row in mat:
        for a in row:
            s += a
            s %= md
    ans = ans*s%md
print(ans)
 
 
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