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 198 ms / 2,000 ms
コード長 4,116 bytes
コンパイル時間 293 ms
コンパイル使用メモリ 86,900 KB
実行使用メモリ 81,500 KB
最終ジャッジ日時 2023-09-30 12:53:06
合計ジャッジ時間 13,072 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge11
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 188 ms
80,556 KB
testcase_01 AC 189 ms
80,696 KB
testcase_02 AC 187 ms
80,664 KB
testcase_03 AC 191 ms
80,712 KB
testcase_04 AC 190 ms
80,736 KB
testcase_05 AC 189 ms
80,808 KB
testcase_06 AC 186 ms
80,624 KB
testcase_07 AC 188 ms
80,464 KB
testcase_08 AC 188 ms
80,708 KB
testcase_09 AC 192 ms
80,584 KB
testcase_10 AC 193 ms
80,492 KB
testcase_11 AC 190 ms
81,028 KB
testcase_12 AC 194 ms
81,028 KB
testcase_13 AC 189 ms
80,940 KB
testcase_14 AC 190 ms
81,048 KB
testcase_15 AC 197 ms
80,956 KB
testcase_16 AC 198 ms
81,024 KB
testcase_17 AC 189 ms
80,860 KB
testcase_18 AC 190 ms
81,036 KB
testcase_19 AC 189 ms
81,024 KB
testcase_20 AC 190 ms
81,120 KB
testcase_21 AC 189 ms
80,568 KB
testcase_22 AC 190 ms
80,712 KB
testcase_23 AC 190 ms
80,796 KB
testcase_24 AC 185 ms
80,552 KB
testcase_25 AC 191 ms
80,952 KB
testcase_26 AC 190 ms
80,928 KB
testcase_27 AC 186 ms
81,088 KB
testcase_28 AC 185 ms
80,964 KB
testcase_29 AC 190 ms
80,972 KB
testcase_30 AC 190 ms
81,092 KB
testcase_31 AC 191 ms
81,008 KB
testcase_32 AC 189 ms
80,632 KB
testcase_33 AC 189 ms
81,116 KB
testcase_34 AC 191 ms
81,004 KB
testcase_35 AC 189 ms
81,004 KB
testcase_36 AC 190 ms
80,512 KB
testcase_37 AC 192 ms
80,828 KB
testcase_38 AC 194 ms
80,940 KB
testcase_39 AC 191 ms
81,024 KB
testcase_40 AC 193 ms
80,944 KB
testcase_41 AC 192 ms
81,500 KB
testcase_42 AC 195 ms
81,116 KB
testcase_43 AC 191 ms
80,992 KB
testcase_44 AC 190 ms
81,268 KB
testcase_45 AC 191 ms
81,132 KB
testcase_46 AC 190 ms
81,012 KB
testcase_47 AC 192 ms
81,088 KB
testcase_48 AC 192 ms
81,032 KB
testcase_49 AC 193 ms
80,844 KB
testcase_50 AC 188 ms
81,036 KB
testcase_51 AC 189 ms
80,792 KB
testcase_52 AC 188 ms
80,576 KB
testcase_53 AC 187 ms
80,740 KB
testcase_54 AC 190 ms
80,668 KB
testcase_55 AC 189 ms
80,668 KB
権限があれば一括ダウンロードができます

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