結果

問題 No.1973 Divisor Sequence
ユーザー chineristACchineristAC
提出日時 2022-06-10 21:49:09
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 97 ms / 2,000 ms
コード長 2,951 bytes
コンパイル時間 165 ms
コンパイル使用メモリ 81,632 KB
実行使用メモリ 77,024 KB
最終ジャッジ日時 2023-10-21 06:19:27
合計ジャッジ時間 2,546 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge11
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 51 ms
58,300 KB
testcase_01 AC 49 ms
58,300 KB
testcase_02 AC 50 ms
58,300 KB
testcase_03 AC 49 ms
58,300 KB
testcase_04 AC 50 ms
58,300 KB
testcase_05 AC 49 ms
58,300 KB
testcase_06 AC 51 ms
58,300 KB
testcase_07 AC 49 ms
58,300 KB
testcase_08 AC 52 ms
58,300 KB
testcase_09 AC 50 ms
58,300 KB
testcase_10 AC 54 ms
63,652 KB
testcase_11 AC 49 ms
58,300 KB
testcase_12 AC 49 ms
58,300 KB
testcase_13 AC 50 ms
58,300 KB
testcase_14 AC 63 ms
66,760 KB
testcase_15 AC 51 ms
58,300 KB
testcase_16 AC 50 ms
58,300 KB
testcase_17 AC 53 ms
63,652 KB
testcase_18 AC 57 ms
64,648 KB
testcase_19 AC 55 ms
64,640 KB
testcase_20 AC 50 ms
58,300 KB
testcase_21 AC 51 ms
58,300 KB
testcase_22 AC 51 ms
58,300 KB
testcase_23 AC 97 ms
77,024 KB
testcase_24 AC 67 ms
70,896 KB
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ソースコード

diff # 

def isPrimeMR(n):
    if n==1:
        return 0
    d = n - 1
    d = d // (d & -d)
    L = [2, 3, 5, 7, 11, 13, 17]
    if n in L:
        return 1
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1: continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1: return 0
            t <<= 1
    return 1
def findFactorRho(n):
    from math import gcd
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g): return g
            elif isPrimeMR(n // g): return n // g
            return findFactorRho(g)
def primeFactor(n):
    i = 2
    ret = {}
    rhoFlg = 0
    while i*i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k: ret[i] = k
        i += 1 + i % 2
        if i == 101 and n >= 2 ** 20:
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    rhoFlg = 1
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k

    if n > 1: ret[n] = 1
    if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
    return ret

import sys,random,bisect
from collections import deque,defaultdict,Counter
from heapq import heapify,heappop,heappush
from itertools import cycle, permutations
from math import log,gcd

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

mod = 10**9 + 7

def mat_mul(X,Y):
    n,m = len(X),len(Y[0])
    res = [[0 for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            for k in range(len(Y)):
                res[i][j] += X[i][k] * Y[k][j]
                res[i][j] %= mod
    return res

N,M = mi()

pf = primeFactor(M)

res = 1
for p in pf:
    e = pf[p]
    A = [[0 for j in range(e+1)] for i in range(e+1)]
    for i in range(e+1):
        for j in range(e+1):
            if i+j <= e:
                A[j][i] = 1
    E = [[1] for i in range(e+1)]
    tmp = N-1
    while tmp:
        if tmp&1:
            E = mat_mul(A,E)
        A = mat_mul(A,A)
        tmp >>= 1
    s = 0
    for i in range(e+1):
        s += E[i][0]
        s %= mod
    res *= s
    res %= mod

print(res)
0