結果

問題 No.1388 Less than K
ユーザー vwxyzvwxyz
提出日時 2023-11-19 01:45:41
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,936 ms / 3,000 ms
コード長 4,460 bytes
コンパイル時間 397 ms
コンパイル使用メモリ 82,160 KB
実行使用メモリ 130,108 KB
最終ジャッジ日時 2024-09-26 06:04:32
合計ジャッジ時間 54,613 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 123 ms
89,560 KB
testcase_01 AC 123 ms
89,460 KB
testcase_02 AC 129 ms
89,928 KB
testcase_03 AC 125 ms
89,460 KB
testcase_04 AC 134 ms
90,132 KB
testcase_05 AC 158 ms
90,504 KB
testcase_06 AC 151 ms
90,516 KB
testcase_07 AC 126 ms
89,936 KB
testcase_08 AC 181 ms
91,920 KB
testcase_09 AC 148 ms
90,576 KB
testcase_10 AC 146 ms
90,524 KB
testcase_11 AC 152 ms
90,604 KB
testcase_12 AC 184 ms
92,312 KB
testcase_13 AC 202 ms
93,488 KB
testcase_14 AC 236 ms
94,520 KB
testcase_15 AC 378 ms
98,016 KB
testcase_16 AC 467 ms
100,972 KB
testcase_17 AC 638 ms
104,152 KB
testcase_18 AC 977 ms
111,756 KB
testcase_19 AC 1,379 ms
117,960 KB
testcase_20 AC 1,477 ms
118,176 KB
testcase_21 AC 226 ms
117,864 KB
testcase_22 AC 180 ms
112,088 KB
testcase_23 AC 169 ms
99,660 KB
testcase_24 AC 191 ms
105,432 KB
testcase_25 AC 202 ms
108,032 KB
testcase_26 AC 196 ms
109,864 KB
testcase_27 AC 183 ms
103,816 KB
testcase_28 AC 170 ms
104,988 KB
testcase_29 AC 164 ms
105,004 KB
testcase_30 AC 145 ms
90,412 KB
testcase_31 AC 152 ms
94,068 KB
testcase_32 AC 130 ms
89,608 KB
testcase_33 AC 175 ms
115,184 KB
testcase_34 AC 176 ms
114,656 KB
testcase_35 AC 174 ms
112,156 KB
testcase_36 AC 217 ms
115,100 KB
testcase_37 AC 193 ms
118,260 KB
testcase_38 AC 270 ms
118,336 KB
testcase_39 AC 211 ms
114,968 KB
testcase_40 AC 238 ms
112,208 KB
testcase_41 AC 358 ms
129,120 KB
testcase_42 AC 212 ms
118,360 KB
testcase_43 AC 1,243 ms
129,176 KB
testcase_44 AC 2,134 ms
128,356 KB
testcase_45 AC 1,602 ms
129,024 KB
testcase_46 AC 2,071 ms
129,488 KB
testcase_47 AC 2,765 ms
125,204 KB
testcase_48 AC 2,381 ms
129,152 KB
testcase_49 AC 2,936 ms
128,672 KB
testcase_50 AC 2,760 ms
128,544 KB
testcase_51 AC 1,682 ms
129,028 KB
testcase_52 AC 1,393 ms
129,056 KB
testcase_53 AC 485 ms
129,928 KB
testcase_54 AC 319 ms
129,360 KB
testcase_55 AC 197 ms
129,196 KB
testcase_56 AC 680 ms
129,936 KB
testcase_57 AC 1,649 ms
129,884 KB
testcase_58 AC 2,806 ms
129,180 KB
testcase_59 AC 1,720 ms
129,172 KB
testcase_60 AC 1,354 ms
129,204 KB
testcase_61 AC 231 ms
129,152 KB
testcase_62 AC 190 ms
121,688 KB
testcase_63 AC 218 ms
129,792 KB
testcase_64 AC 239 ms
130,108 KB
testcase_65 AC 317 ms
129,776 KB
testcase_66 AC 498 ms
129,748 KB
testcase_67 AC 450 ms
129,380 KB
testcase_68 AC 1,222 ms
129,784 KB
testcase_69 AC 1,420 ms
129,992 KB
testcase_70 AC 2,224 ms
128,956 KB
testcase_71 AC 2,202 ms
129,224 KB
testcase_72 AC 251 ms
129,164 KB
testcase_73 AC 240 ms
129,388 KB
testcase_74 AC 232 ms
129,400 KB
testcase_75 AC 216 ms
129,172 KB
testcase_76 AC 208 ms
129,312 KB
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ソースコード

diff # 

import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
import time
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 gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
write=sys.stdout.write
#import pypyjit
#pypyjit.set_param('max_unroll_recursion=-1')
#sys.set_int_max_str_digits(10**9)

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=None):
        self.p=p
        self.e=e
        if self.e==None:
            self.mod=self.p
        else:
            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]
        if self.e==None:
            for i in range(1,N+1):
                self.factorial.append(self.factorial[-1]*i%self.mod)
        else:
            self.cnt=[0]*(N+1)
            for i in range(1,N+1):
                self.cnt[i]=self.cnt[i-1]
                ii=i
                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 Build_Inverse(self,N):
        self.inverse=[None]*(N+1)
        assert self.p>N
        self.inverse[1]=1
        for n in range(2,N+1):
            if n%self.p==0:
                continue
            a,b=divmod(self.mod,n)
            self.inverse[n]=(-a*self.inverse[b])%self.mod
    
    def Inverse(self,n):
        return self.inverse[n]

    def Fact(self,N):
        if N<0:
            return 0
        retu=self.factorial[N]
        if self.e!=None and self.cnt[N]:
            retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
            retu%=self.mod
        return retu

    def Fact_Inve(self,N):
        if self.e!=None and 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.mod*self.factorial_inve[N-K]%self.mod
        if self.e!=None:
            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

H,W,K=map(int,readline().split())
H-=1;W-=1
K//=2
mod=998244353
MD=MOD(mod)
MD.Build_Fact(H+W)
N=min(H,W)
ans=0
if K<=300:
    for h in range(N+1):
        if h:
            prev=dp
            dp=[0]*(2*K+1)
        else:
            dp=[0]*(2*K+1)
            dp[K]=1
        for w in range(max(h-K,0),min(h+K,N)+1):
            if h and abs((h-1)-w)<=K:
                dp[w-h+K]+=prev[w-(h-1)+K]
            if w and abs(h-(w-1))<=K:
                dp[w-h+K]+=dp[(w-1)-h+K]
            dp[w-h+K]%=mod
        ans+=MD.Fact(H+W)*MD.Fact_Inve(H-h)%mod*MD.Fact_Inve(W-h)%mod*MD.Fact_Inve(2*h)%mod*dp[K]%mod
        ans%=mod
else:
    for cnt in range(N+1):
        s=MD.Comb(2*cnt,cnt)
        for i in range(1,cnt//(K+1)+1):
            if i%2:
                s-=2*MD.Comb(2*cnt,cnt-(K+1)*i)
            else:
                s+=2*MD.Comb(2*cnt,cnt-(K+1)*i)
            s%=mod
        ans+=MD.Fact(H+W)*MD.Fact_Inve(H-cnt)%mod*MD.Fact_Inve(W-cnt)%mod*MD.Fact_Inve(2*cnt)%mod*s%mod
        ans%=mod
print(ans)
0