結果

問題 No.2487 Multiple of M
ユーザー prin_kemkemprin_kemkem
提出日時 2023-09-30 00:04:46
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 4,062 bytes
コンパイル時間 270 ms
コンパイル使用メモリ 87,212 KB
実行使用メモリ 81,456 KB
最終ジャッジ日時 2023-09-30 12:52:49
合計ジャッジ時間 12,965 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 192 ms
80,464 KB
testcase_01 AC 191 ms
80,764 KB
testcase_02 AC 189 ms
80,852 KB
testcase_03 AC 190 ms
80,680 KB
testcase_04 AC 190 ms
80,588 KB
testcase_05 AC 189 ms
80,800 KB
testcase_06 AC 189 ms
80,572 KB
testcase_07 AC 189 ms
80,624 KB
testcase_08 AC 187 ms
80,920 KB
testcase_09 AC 190 ms
80,696 KB
testcase_10 AC 188 ms
80,600 KB
testcase_11 AC 187 ms
80,836 KB
testcase_12 AC 190 ms
80,944 KB
testcase_13 AC 192 ms
81,016 KB
testcase_14 AC 189 ms
81,044 KB
testcase_15 AC 190 ms
81,096 KB
testcase_16 AC 189 ms
81,292 KB
testcase_17 AC 188 ms
80,724 KB
testcase_18 AC 190 ms
80,912 KB
testcase_19 AC 189 ms
80,940 KB
testcase_20 AC 188 ms
80,996 KB
testcase_21 AC 188 ms
80,784 KB
testcase_22 AC 188 ms
80,856 KB
testcase_23 AC 191 ms
80,820 KB
testcase_24 AC 189 ms
80,804 KB
testcase_25 AC 190 ms
81,112 KB
testcase_26 AC 188 ms
81,012 KB
testcase_27 AC 192 ms
81,060 KB
testcase_28 AC 191 ms
81,008 KB
testcase_29 WA -
testcase_30 AC 191 ms
80,952 KB
testcase_31 AC 193 ms
80,980 KB
testcase_32 AC 189 ms
80,540 KB
testcase_33 AC 189 ms
80,960 KB
testcase_34 AC 187 ms
81,152 KB
testcase_35 AC 191 ms
81,004 KB
testcase_36 AC 192 ms
80,648 KB
testcase_37 AC 191 ms
81,260 KB
testcase_38 AC 192 ms
81,040 KB
testcase_39 AC 191 ms
80,980 KB
testcase_40 AC 189 ms
81,164 KB
testcase_41 AC 190 ms
81,456 KB
testcase_42 AC 190 ms
80,940 KB
testcase_43 AC 191 ms
80,832 KB
testcase_44 AC 189 ms
81,032 KB
testcase_45 AC 191 ms
81,064 KB
testcase_46 AC 190 ms
81,084 KB
testcase_47 AC 192 ms
81,036 KB
testcase_48 AC 191 ms
81,156 KB
testcase_49 AC 191 ms
81,052 KB
testcase_50 AC 189 ms
81,068 KB
testcase_51 AC 187 ms
80,660 KB
testcase_52 AC 188 ms
80,808 KB
testcase_53 AC 188 ms
80,500 KB
testcase_54 AC 187 ms
80,484 KB
testcase_55 AC 185 ms
80,664 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])
        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])
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