結果

問題 No.1388 Less than K
ユーザー vwxyzvwxyz
提出日時 2023-11-19 02:34:48
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,953 bytes
コンパイル時間 342 ms
コンパイル使用メモリ 81,828 KB
実行使用メモリ 91,756 KB
最終ジャッジ日時 2023-11-19 02:35:31
合計ジャッジ時間 41,914 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge13
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 37 ms
53,460 KB
testcase_01 AC 37 ms
53,460 KB
testcase_02 AC 45 ms
61,852 KB
testcase_03 AC 37 ms
53,460 KB
testcase_04 AC 52 ms
64,052 KB
testcase_05 AC 89 ms
76,376 KB
testcase_06 AC 72 ms
73,308 KB
testcase_07 AC 45 ms
61,852 KB
testcase_08 AC 102 ms
76,252 KB
testcase_09 AC 67 ms
71,224 KB
testcase_10 AC 64 ms
71,228 KB
testcase_11 AC 62 ms
68,628 KB
testcase_12 AC 98 ms
76,792 KB
testcase_13 AC 119 ms
77,468 KB
testcase_14 AC 149 ms
77,692 KB
testcase_15 AC 299 ms
79,216 KB
testcase_16 AC 396 ms
80,276 KB
testcase_17 AC 609 ms
81,728 KB
testcase_18 AC 979 ms
84,348 KB
testcase_19 AC 1,392 ms
86,676 KB
testcase_20 AC 1,474 ms
87,236 KB
testcase_21 AC 122 ms
87,404 KB
testcase_22 AC 68 ms
76,240 KB
testcase_23 AC 79 ms
78,212 KB
testcase_24 AC 101 ms
81,896 KB
testcase_25 AC 112 ms
83,216 KB
testcase_26 AC 102 ms
83,916 KB
testcase_27 AC 83 ms
80,288 KB
testcase_28 AC 63 ms
72,380 KB
testcase_29 AC 62 ms
72,180 KB
testcase_30 AC 52 ms
64,296 KB
testcase_31 AC 55 ms
66,840 KB
testcase_32 AC 45 ms
61,848 KB
testcase_33 AC 70 ms
77,580 KB
testcase_34 AC 68 ms
76,800 KB
testcase_35 AC 67 ms
76,024 KB
testcase_36 AC 82 ms
83,160 KB
testcase_37 AC 72 ms
79,200 KB
testcase_38 AC 159 ms
87,480 KB
testcase_39 AC 105 ms
85,780 KB
testcase_40 AC 132 ms
84,988 KB
testcase_41 AC 250 ms
91,340 KB
testcase_42 AC 97 ms
87,464 KB
testcase_43 AC 504 ms
91,032 KB
testcase_44 AC 2,262 ms
91,116 KB
testcase_45 AC 646 ms
90,864 KB
testcase_46 AC 809 ms
89,064 KB
testcase_47 AC 2,890 ms
90,856 KB
testcase_48 AC 2,452 ms
91,468 KB
testcase_49 TLE -
testcase_50 AC 2,893 ms
91,076 KB
testcase_51 AC 670 ms
90,904 KB
testcase_52 AC 581 ms
91,072 KB
testcase_53 AC 369 ms
91,548 KB
testcase_54 AC 211 ms
91,240 KB
testcase_55 AC 81 ms
91,016 KB
testcase_56 AC 619 ms
91,636 KB
testcase_57 AC 1,644 ms
91,628 KB
testcase_58 AC 2,883 ms
91,616 KB
testcase_59 AC 699 ms
91,144 KB
testcase_60 AC 589 ms
91,172 KB
testcase_61 AC 91 ms
89,056 KB
testcase_62 AC 72 ms
79,980 KB
testcase_63 AC 102 ms
91,604 KB
testcase_64 AC 126 ms
91,640 KB
testcase_65 AC 214 ms
91,640 KB
testcase_66 AC 373 ms
91,688 KB
testcase_67 AC 362 ms
91,336 KB
testcase_68 AC 1,192 ms
91,636 KB
testcase_69 AC 1,385 ms
91,756 KB
testcase_70 AC 2,275 ms
91,616 KB
testcase_71 AC 802 ms
89,352 KB
testcase_72 AC 103 ms
91,616 KB
testcase_73 AC 92 ms
89,568 KB
testcase_74 AC 88 ms
86,748 KB
testcase_75 AC 79 ms
82,060 KB
testcase_76 AC 79 ms
82,060 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<=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+=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]%mod*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