結果

問題 No.1414 東大文系数学2021第2問改
ユーザー vwxyzvwxyz
提出日時 2024-05-03 15:40:11
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 642 ms / 2,000 ms
コード長 3,055 bytes
コンパイル時間 230 ms
コンパイル使用メモリ 82,480 KB
実行使用メモリ 254,952 KB
最終ジャッジ日時 2024-11-24 17:42:54
合計ジャッジ時間 17,510 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
other AC * 27
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 #
プレゼンテーションモードにする

import bisect
import copy
import decimal
import fractions
import functools
import heapq
import itertools
import math
import random
import sys
from collections import Counter,deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
heap.append(item)
heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
if heap and item < heap[0]:
item, heap[0] = heap[0], item
heapq._siftup_max(heap, 0)
return item
from math import degrees, gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
def Extended_Euclid(n,m):
stack=[]
while m:
stack.append((n,m))
n,m=m,n%m
if n>=0:
x,y=1,0
else:
x,y=-1,0
for i in range(len(stack)-1,-1,-1):
n,m=stack[i]
x,y=y,x-(n//m)*y
return x,y
class MOD:
def __init__(self,p,e=1):
self.p=p
self.e=e
self.mod=self.p**self.e
def Pow(self,a,n):
a%=self.mod
if n>=0:
return pow(a,n,self.mod)
else:
assert math.gcd(a,self.mod)==1
x=Extended_Euclid(a,self.mod)[0]
return pow(x,-n,self.mod)
def Build_Fact(self,N):
assert N>=0
self.factorial=[1]
self.cnt=[0]*(N+1)
for i in range(1,N+1):
ii=i
self.cnt[i]=self.cnt[i-1]
while ii%self.p==0:
ii//=self.p
self.cnt[i]+=1
self.factorial.append((self.factorial[-1]*ii)%self.mod)
self.factorial_inve=[None]*(N+1)
self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
for i in range(N-1,-1,-1):
ii=i+1
while ii%self.p==0:
ii//=self.p
self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod
def Fact(self,N):
return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod
def Fact_Inve(self,N):
if self.cnt[N]:
return None
return self.factorial_inve[N]
def Comb(self,N,K,divisible_count=False):
if K<0 or K>N:
return 0
retu=self.factorial[N]*self.factorial_inve[K]*self.factorial_inve[N-K]%self.mod
cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
if divisible_count:
return retu,cnt
else:
retu*=pow(self.p,cnt,self.mod)
retu%=self.mod
return retu
N,M,K=map(int,readline().split())
mod=998244353
fact=[1]
for i in range(1,10000001):
fact.append(fact[-1]*i%mod)
fact_inve=[1]*10000001
fact_inve[10000000]=759799589
for i in range(9999999,0,-1):
fact_inve[i]=fact_inve[i+1]*(i+1)%mod
def Comb(a,b):
if a<b or b<0:
return 0
return fact[a]*fact_inve[b]%mod*fact_inve[a-b]%mod
ans=0
for i in range(1,min(M//K,N-M+1)+1):
if i%2==1:
ans+=Comb(N-i*K,N-M)*Comb(N-M+1,i)
else:
ans-=Comb(N-i*K,N-M)*Comb(N-M+1,i)
ans%=mod
print(ans)
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