結果

問題 No.2487 Multiple of M
ユーザー prin_kemkemprin_kemkem
提出日時 2023-09-30 00:20:51
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 106 ms / 2,000 ms
コード長 4,116 bytes
コンパイル時間 215 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 80,892 KB
最終ジャッジ日時 2024-07-23 06:56:20
合計ジャッジ時間 7,277 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
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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 96 ms
80,128 KB
testcase_01 AC 96 ms
80,512 KB
testcase_02 AC 93 ms
80,512 KB
testcase_03 AC 104 ms
80,384 KB
testcase_04 AC 96 ms
80,276 KB
testcase_05 AC 97 ms
80,000 KB
testcase_06 AC 97 ms
80,256 KB
testcase_07 AC 97 ms
80,128 KB
testcase_08 AC 96 ms
80,512 KB
testcase_09 AC 100 ms
80,292 KB
testcase_10 AC 97 ms
80,512 KB
testcase_11 AC 99 ms
80,256 KB
testcase_12 AC 98 ms
80,640 KB
testcase_13 AC 100 ms
80,640 KB
testcase_14 AC 100 ms
80,220 KB
testcase_15 AC 99 ms
80,256 KB
testcase_16 AC 100 ms
80,512 KB
testcase_17 AC 97 ms
80,356 KB
testcase_18 AC 102 ms
80,640 KB
testcase_19 AC 99 ms
80,512 KB
testcase_20 AC 97 ms
80,512 KB
testcase_21 AC 96 ms
80,256 KB
testcase_22 AC 96 ms
80,428 KB
testcase_23 AC 97 ms
80,128 KB
testcase_24 AC 99 ms
80,256 KB
testcase_25 AC 98 ms
80,512 KB
testcase_26 AC 100 ms
80,512 KB
testcase_27 AC 97 ms
80,512 KB
testcase_28 AC 98 ms
80,640 KB
testcase_29 AC 99 ms
80,384 KB
testcase_30 AC 98 ms
80,400 KB
testcase_31 AC 99 ms
80,640 KB
testcase_32 AC 102 ms
80,000 KB
testcase_33 AC 98 ms
80,616 KB
testcase_34 AC 98 ms
80,512 KB
testcase_35 AC 97 ms
80,508 KB
testcase_36 AC 99 ms
80,256 KB
testcase_37 AC 97 ms
80,268 KB
testcase_38 AC 100 ms
80,128 KB
testcase_39 AC 100 ms
80,512 KB
testcase_40 AC 96 ms
80,512 KB
testcase_41 AC 98 ms
80,892 KB
testcase_42 AC 105 ms
80,640 KB
testcase_43 AC 102 ms
80,512 KB
testcase_44 AC 97 ms
80,384 KB
testcase_45 AC 99 ms
80,384 KB
testcase_46 AC 100 ms
80,640 KB
testcase_47 AC 106 ms
80,128 KB
testcase_48 AC 97 ms
80,128 KB
testcase_49 AC 99 ms
80,640 KB
testcase_50 AC 98 ms
80,256 KB
testcase_51 AC 95 ms
80,380 KB
testcase_52 AC 95 ms
80,384 KB
testcase_53 AC 96 ms
80,512 KB
testcase_54 AC 98 ms
80,512 KB
testcase_55 AC 96 ms
80,512 KB
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ソースコード

diff # 

from collections import defaultdict, deque, Counter
import copy
from itertools import combinations, permutations, product, accumulate, groupby, chain
from heapq import heapify, heappop, heappush
import math
import bisect
from pprint import pprint
from random import randint
import sys
# sys.setrecursionlimit(700000)
input = lambda: sys.stdin.readline().rstrip('\n')
inf = float('inf')
mod1 = 10**9+7
mod2 = 998244353
def ceil_div(x, y): return -(-x//y)

#################################################

class Matrix():
    def __init__(self, mat, mod=None):
        self.mat = mat
        self.n = len(mat)
        self.m = len(mat[0])
        self.mod = mod
    def __mul__(self, other):
        ret = Matrix([[0]*other.m for _ in range(self.n)], self.mod)
        for i in range(self.n):
            for j in range(other.m):
                for k in range(self.m):
                    ret[i][j] += self.mat[i][k]*other.mat[k][j]
                    if self.mod is not None: ret[i][j] %= self.mod
        return ret
    def __add__(self, other):
        ret = Matrix([[self.mat[i][j] for j in range(self.m)] for i in range(self.n)], self.mod)
        for i in range(other.n):
            for j in range(other.m):
                ret[i][j] += other.mat[i][j]
                if self.mod is not None: ret[i][j] %= self.mod
        return ret
    def __sub__(self, other):
        ret = Matrix([[self.mat[i][j] for j in range(self.m)] for i in range(self.n)], self.mod)
        for i in range(other.n):
            for j in range(other.m):
                ret[i][j] -= other.mat[i][j]
                if self.mod is not None: ret[i][j] %= self.mod
        return ret
    def __pow__(self, scalar):
        a = Matrix([[self.mat[i][j] for j in range(self.m)] for i in range(self.n)], self.mod)
        ret = Matrix.e(self.n, self.mod)
        while scalar:
            if scalar&1:
                ret *= a
            a *= a
            scalar >>= 1
        return ret
    def scalar_mul(self, a):
        ret = Matrix([[self.mat[i][j] for j in range(self.m)] for i in range(self.n)], self.mod)
        for i in range(self.n):
            for j in range(self.m):
                ret[i][j] *= a
                if self.mod is not None: ret[i][j] %= self.mod
        return ret
    def __repr__(self) -> str:
        return self.mat.__repr__()
    def __getitem__(self, i):
        return self.mat[i]
    def __setitem__(self, i, x):
        self.mat[i] = x
    def __len__(self):
        return len(self.mat)
    def t(self):
        return Matrix([list(column) for column in zip(*self.mat)], self.mod)
    def turn(matrix):
        if type(matrix) != 'Matrix':
            return Matrix([list(column) for column in zip(*matrix)])
        return Matrix([list(column) for column in zip(*matrix.mat)], matrix.mod)
    def e(size, mod):
        return Matrix([[i == j for j in range(size)] for i in range(size)], mod)

def prime_factorize(n):
    ret = defaultdict(int)
    i = 2
    while i*i <= n:
        if n%i == 0:
            ret[i] += 1
            n //= i
        else:
            i += 1
    if n != 1:
        ret[n] += 1
    return ret

N, M, K = map(int, input().split())
a = Matrix([[0], [1]], mod=mod2)
if K == 1:
    d = 1
    l = M
    A = Matrix([[d-1, d*(l-1)%mod2], [d, (d-1+d*(l-2))%mod2]], mod=mod2)
    a = A**(N-1) * a
    print(a[0][0])
    exit()
PM, PK = prime_factorize(M), prime_factorize(K)
x = 0
s = {}
for p, e in PM.items():
    if PK[p] == 0: continue
    s[p] = PK[p]
    x = max(x, ceil_div(e, PK[p]))
i = 0
while i < min(x, N-1):
    d = 1
    for p, e in s.items():
        d *= p**min(PM[p], e*(i+1))
    l = M//d
    if l == 1:
        print(a[0][0]*pow(M-1, N-1-i, mod2)%mod2)
        exit()
    A = Matrix([[d-1, d*(l-1)%mod2], [d, (d-1+d*(l-2))%mod2]], mod=mod2)
    a = A*a
    i += 1
if i == N-1:
    print(a[0][0])
    exit()
d = 1
for p, e in s.items():
    d *= p**min(PM[p], e*(i+1))
l = M//d
if l == 1:
    print(a[0][0]*pow(M-1, N-1-i, mod2)%mod2)
else:
    A = Matrix([[d-1, d*(l-1)%mod2], [d, (d-1+d*(l-2))%mod2]], mod=mod2)
    a = A**(N-1-i) * a
    print(a[0][0])
0