結果

問題 No.3160 Party Game
ユーザー lif4635
提出日時 2025-05-23 20:21:05
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 287 ms / 2,000 ms
コード長 4,477 bytes
コンパイル時間 244 ms
コンパイル使用メモリ 82,376 KB
実行使用メモリ 116,140 KB
最終ジャッジ日時 2025-05-27 22:01:18
合計ジャッジ時間 8,419 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 38
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 # 

# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]

def graph(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[int]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b = map(int, input().split())
        a += index
        b += index
        edge[a].add(b)
        if not dir:
            edge[b].add(a)
    return edge

def graph_w(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[tuple]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b,c = map(int, input().split())
        a += index
        b += index
        edge[a].add((b,c))
        if not dir:
            edge[b].add((a,c))
    return edge

mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
def acc(a:list[int]):
    sa = [0]*(len(a)+1)
    for i in range(len(a)):
        sa[i+1] = a[i] + sa[i]
    return sa

prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')

from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right

class Comb:
    __slots__ = ["fac", "finv", "mod"]
    def __init__(self, lim:int, mod:int = mod):
        """
        mod : prime
        """
        self.fac = [1]*(lim+1)
        self.finv = [1]*(lim+1)
        self.mod = mod
        for i in range(2,lim+1):
            self.fac[i] = self.fac[i-1]*i%self.mod
        self.finv[lim] = pow(self.fac[lim],-1,mod)
        for i in range(lim,2,-1):
            self.finv[i-1] = self.finv[i]*i%self.mod
    
    def C(self, a, b):
        assert b >= 0, "The second argument is negative."
        if a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[b]%self.mod*self.finv[a-b]%self.mod
    
    def P(self, a, b):
        assert b >= 0, "The second argument is negative."
        if a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[a-b]%self.mod
    
    def H(self, a, b): return self.C(a+b-1,b)
    def F(self, a): return self.fac[a]
    def Fi(self, a): return self.finv[a]
    def __call__(self, a, b): return self.C(a, b)



# 全員の総和がM以下のときのminの期待値

n, m = MI()
comb = Comb(2 * 10 ** 6)
# 総和s以下、n人、m以下 
sgn = [1, -1]

lim = max(n, m)
# 負の二項係数の分
q = [1] * (lim + 1)
for k in range(1, lim + 1):
    q[k] = comb(n + k - 1, n - 1)

# 累積和にしておく
for i in range(lim):
    q[i+1] = (q[i+1] + q[i]) % mod
# print(q)

def calc(s, n, m):
    ans = 0
    for k in range(s + 1):
        if s < k * m: break
        ans += sgn[k & 1] * comb(n, k) * q[s - (k * m)]
    # print(s, n, m, ans)
    return ans % mod

def calc_naive(s, n, m):
    dp = [[0] * (s + 1) for _ in range(n + 1)]
    dp[0][0] = 1
    for i in range(1, n + 1):
        for j in range(s + 1):
            for k in range(0, m + 1):
                if j - k >= 0:
                    dp[i][j] += dp[i - 1][j - k]
    return sum(dp[n][j] for j in range(s + 1))

# for n in range(1, 5):
#     for m in range(1, 5):
#         for s in range(10):
#             print(s,n,m,calc_naive(s, n, m), calc(s, n, m))

ans = 0
for mi in range(1, m):
    # min が mi 以上となる通り数
    if m < n * mi: break
    r = calc(m - n * mi, n, m - mi)
    # print(r)
    ans += r

ans = ans * pow(calc(m, n, m), -1, mod) % mod
print(ans)
0