結果

問題 No.1388 Less than K
ユーザー vwxyzvwxyz
提出日時 2023-11-19 02:37:33
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,965 ms / 3,000 ms
コード長 3,949 bytes
コンパイル時間 374 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 92,288 KB
最終ジャッジ日時 2024-09-26 06:12:40
合計ジャッジ時間 40,987 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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 40 ms
53,120 KB
testcase_01 AC 39 ms
52,736 KB
testcase_02 AC 45 ms
60,800 KB
testcase_03 AC 39 ms
53,376 KB
testcase_04 AC 54 ms
64,128 KB
testcase_05 AC 84 ms
76,800 KB
testcase_06 AC 75 ms
73,344 KB
testcase_07 AC 44 ms
60,672 KB
testcase_08 AC 103 ms
76,544 KB
testcase_09 AC 69 ms
71,168 KB
testcase_10 AC 65 ms
70,916 KB
testcase_11 AC 63 ms
69,120 KB
testcase_12 AC 96 ms
77,312 KB
testcase_13 AC 119 ms
77,696 KB
testcase_14 AC 146 ms
78,208 KB
testcase_15 AC 286 ms
79,616 KB
testcase_16 AC 376 ms
80,876 KB
testcase_17 AC 565 ms
82,048 KB
testcase_18 AC 914 ms
84,864 KB
testcase_19 AC 1,307 ms
87,320 KB
testcase_20 AC 1,394 ms
87,808 KB
testcase_21 AC 119 ms
87,980 KB
testcase_22 AC 70 ms
74,368 KB
testcase_23 AC 78 ms
77,824 KB
testcase_24 AC 98 ms
82,432 KB
testcase_25 AC 109 ms
83,792 KB
testcase_26 AC 94 ms
84,396 KB
testcase_27 AC 80 ms
80,256 KB
testcase_28 AC 63 ms
72,576 KB
testcase_29 AC 61 ms
71,808 KB
testcase_30 AC 53 ms
64,384 KB
testcase_31 AC 56 ms
67,328 KB
testcase_32 AC 46 ms
60,416 KB
testcase_33 AC 67 ms
75,648 KB
testcase_34 AC 68 ms
74,752 KB
testcase_35 AC 69 ms
74,112 KB
testcase_36 AC 83 ms
81,792 KB
testcase_37 AC 70 ms
77,440 KB
testcase_38 AC 166 ms
87,936 KB
testcase_39 AC 117 ms
86,272 KB
testcase_40 AC 135 ms
85,248 KB
testcase_41 AC 261 ms
91,648 KB
testcase_42 AC 111 ms
88,064 KB
testcase_43 AC 518 ms
91,520 KB
testcase_44 AC 2,120 ms
91,648 KB
testcase_45 AC 597 ms
91,264 KB
testcase_46 AC 797 ms
89,856 KB
testcase_47 AC 2,740 ms
91,392 KB
testcase_48 AC 2,345 ms
91,904 KB
testcase_49 AC 2,965 ms
92,032 KB
testcase_50 AC 2,746 ms
91,904 KB
testcase_51 AC 651 ms
91,136 KB
testcase_52 AC 569 ms
91,264 KB
testcase_53 AC 370 ms
91,904 KB
testcase_54 AC 219 ms
91,776 KB
testcase_55 AC 96 ms
91,520 KB
testcase_56 AC 602 ms
92,032 KB
testcase_57 AC 1,588 ms
92,288 KB
testcase_58 AC 2,762 ms
92,160 KB
testcase_59 AC 698 ms
91,648 KB
testcase_60 AC 569 ms
91,648 KB
testcase_61 AC 105 ms
89,600 KB
testcase_62 AC 80 ms
78,208 KB
testcase_63 AC 110 ms
91,904 KB
testcase_64 AC 133 ms
92,288 KB
testcase_65 AC 222 ms
91,904 KB
testcase_66 AC 364 ms
92,288 KB
testcase_67 AC 365 ms
91,648 KB
testcase_68 AC 1,161 ms
92,160 KB
testcase_69 AC 1,336 ms
92,288 KB
testcase_70 AC 2,175 ms
92,032 KB
testcase_71 AC 808 ms
90,112 KB
testcase_72 AC 112 ms
91,904 KB
testcase_73 AC 100 ms
90,112 KB
testcase_74 AC 97 ms
85,888 KB
testcase_75 AC 86 ms
80,896 KB
testcase_76 AC 89 ms
80,640 KB
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ソースコード

diff # 

import sys
readline=sys.stdin.readline

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
fact=[1]+[i for i in range(1,H+W+1)]
for i in range(1,H+W+1):
    fact[i]*=fact[i-1]
    fact[i]%=mod
fact_inve=[i for i in range(1,H+W+1)]+[pow(fact[H+W],mod-2,mod)]
for i in range(H+W-1,-1,-1):
    fact_inve[i]*=fact_inve[i+1]
    fact_inve[i]%=mod
N=min(H,W)
ans=0
if K<=310:
    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+=fact[H+W]*fact_inve[H-h]%mod*fact_inve[W-h]%mod*fact_inve[2*h]%mod*dp[K]%mod
        ans%=mod
else:
    for cnt in range(N+1):
        s=fact_inve[cnt]*fact_inve[cnt]%mod
        for i in range(1,cnt//(K+1)+1):
            if i%2:
                s-=2*fact_inve[cnt-(K+1)*i]*fact_inve[cnt+(K+1)*i]%mod
            else:
                s+=2*fact_inve[cnt-(K+1)*i]*fact_inve[cnt+(K+1)*i]%mod
            s%=mod
        ans+=fact[H+W]*fact_inve[H-cnt]%mod*fact_inve[W-cnt]%mod*s%mod
        ans%=mod
print(ans)
0