結果

問題 No.2605 Pickup Parentheses
ユーザー 👑 amentorimaruamentorimaru
提出日時 2023-12-04 21:20:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,891 ms / 2,000 ms
コード長 7,415 bytes
コンパイル時間 252 ms
コンパイル使用メモリ 81,700 KB
実行使用メモリ 132,420 KB
最終ジャッジ日時 2024-03-20 19:44:48
合計ジャッジ時間 31,616 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge11
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 41 ms
55,596 KB
testcase_01 AC 45 ms
61,440 KB
testcase_02 AC 44 ms
61,440 KB
testcase_03 AC 115 ms
76,768 KB
testcase_04 AC 105 ms
76,648 KB
testcase_05 AC 125 ms
76,992 KB
testcase_06 AC 128 ms
76,608 KB
testcase_07 AC 121 ms
76,736 KB
testcase_08 AC 126 ms
76,608 KB
testcase_09 AC 102 ms
76,696 KB
testcase_10 AC 122 ms
76,736 KB
testcase_11 AC 107 ms
76,776 KB
testcase_12 AC 102 ms
76,804 KB
testcase_13 AC 79 ms
76,096 KB
testcase_14 AC 105 ms
76,864 KB
testcase_15 AC 115 ms
76,608 KB
testcase_16 AC 85 ms
75,928 KB
testcase_17 AC 104 ms
76,736 KB
testcase_18 AC 899 ms
99,744 KB
testcase_19 AC 464 ms
86,088 KB
testcase_20 AC 167 ms
77,128 KB
testcase_21 AC 156 ms
77,140 KB
testcase_22 AC 129 ms
77,228 KB
testcase_23 AC 752 ms
95,372 KB
testcase_24 AC 227 ms
78,476 KB
testcase_25 AC 1,013 ms
101,456 KB
testcase_26 AC 978 ms
103,112 KB
testcase_27 AC 838 ms
97,240 KB
testcase_28 AC 64 ms
75,696 KB
testcase_29 AC 221 ms
78,384 KB
testcase_30 AC 372 ms
83,736 KB
testcase_31 AC 51 ms
68,528 KB
testcase_32 AC 44 ms
61,392 KB
testcase_33 AC 606 ms
90,880 KB
testcase_34 AC 60 ms
75,696 KB
testcase_35 AC 50 ms
64,392 KB
testcase_36 AC 61 ms
75,696 KB
testcase_37 AC 577 ms
89,072 KB
testcase_38 AC 533 ms
90,944 KB
testcase_39 AC 225 ms
79,976 KB
testcase_40 AC 1,089 ms
108,920 KB
testcase_41 AC 1,090 ms
113,244 KB
testcase_42 AC 1,370 ms
116,792 KB
testcase_43 AC 383 ms
85,544 KB
testcase_44 AC 374 ms
86,772 KB
testcase_45 AC 116 ms
76,832 KB
testcase_46 AC 190 ms
79,628 KB
testcase_47 AC 62 ms
75,328 KB
testcase_48 AC 215 ms
79,308 KB
testcase_49 AC 900 ms
101,048 KB
testcase_50 AC 411 ms
85,936 KB
testcase_51 AC 39 ms
55,596 KB
testcase_52 AC 586 ms
91,588 KB
testcase_53 AC 776 ms
96,580 KB
testcase_54 AC 453 ms
87,232 KB
testcase_55 AC 634 ms
92,280 KB
testcase_56 AC 227 ms
81,080 KB
testcase_57 AC 40 ms
55,596 KB
testcase_58 AC 326 ms
82,352 KB
testcase_59 AC 1,891 ms
132,420 KB
testcase_60 AC 1,180 ms
106,504 KB
testcase_61 AC 874 ms
99,136 KB
testcase_62 AC 736 ms
98,020 KB
testcase_63 AC 902 ms
102,012 KB
testcase_64 AC 695 ms
96,888 KB
testcase_65 AC 1,383 ms
112,824 KB
testcase_66 AC 438 ms
86,912 KB
testcase_67 AC 894 ms
98,800 KB
testcase_68 AC 262 ms
79,892 KB
testcase_69 AC 40 ms
55,596 KB
testcase_70 AC 54 ms
68,160 KB
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 # 

import sys
input = sys.stdin.readline
def read_values(): return tuple(map(int, input().split()))

class FFT():
    def primitive_root_constexpr(self,m):
        if m==2:return 1
        if m==167772161:return 3
        if m==469762049:return 3
        if m==754974721:return 11
        if m==998244353:return 3
        divs=[0]*20
        divs[0]=2
        cnt=1
        x=(m-1)//2
        while(x%2==0):x//=2
        i=3
        while(i*i<=x):
            if (x%i==0):
                divs[cnt]=i
                cnt+=1
                while(x%i==0):
                    x//=i
            i+=2
        if x>1:
            divs[cnt]=x
            cnt+=1
        g=2
        while(1):
            ok=True
            for i in range(cnt):
                if pow(g,(m-1)//divs[i],m)==1:
                    ok=False
                    break
            if ok:
                return g
            g+=1
    def bsf(self,x):
        res=0
        while(x%2==0):
            res+=1
            x//=2
        return res
    rank2=0
    root=[]
    iroot=[]
    rate2=[]
    irate2=[]
    rate3=[]
    irate3=[]
    
    def __init__(self,MOD):
        self.mod=MOD
        self.g=self.primitive_root_constexpr(self.mod)
        self.rank2=self.bsf(self.mod-1)
        self.root=[0 for i in range(self.rank2+1)]
        self.iroot=[0 for i in range(self.rank2+1)]
        self.rate2=[0 for i in range(self.rank2)]
        self.irate2=[0 for i in range(self.rank2)]
        self.rate3=[0 for i in range(self.rank2-1)]
        self.irate3=[0 for i in range(self.rank2-1)]
        self.root[self.rank2]=pow(self.g,(self.mod-1)>>self.rank2,self.mod)
        self.iroot[self.rank2]=pow(self.root[self.rank2],self.mod-2,self.mod)
        for i in range(self.rank2-1,-1,-1):
            self.root[i]=(self.root[i+1]**2)%self.mod
            self.iroot[i]=(self.iroot[i+1]**2)%self.mod
        prod=1;iprod=1
        for i in range(self.rank2-1):
            self.rate2[i]=(self.root[i+2]*prod)%self.mod
            self.irate2[i]=(self.iroot[i+2]*iprod)%self.mod
            prod=(prod*self.iroot[i+2])%self.mod
            iprod=(iprod*self.root[i+2])%self.mod
        prod=1;iprod=1
        for i in range(self.rank2-2):
            self.rate3[i]=(self.root[i+3]*prod)%self.mod
            self.irate3[i]=(self.iroot[i+3]*iprod)%self.mod
            prod=(prod*self.iroot[i+3])%self.mod
            iprod=(iprod*self.root[i+3])%self.mod
    def butterfly(self,a):
        n=len(a)
        h=(n-1).bit_length()
        
        LEN=0
        while(LEN<h):
            if (h-LEN==1):
                p=1<<(h-LEN-1)
                rot=1
                for s in range(1<<LEN):
                    offset=s<<(h-LEN)
                    for i in range(p):
                        l=a[i+offset]
                        r=a[i+offset+p]*rot
                        a[i+offset]=(l+r)%self.mod
                        a[i+offset+p]=(l-r)%self.mod
                    rot*=self.rate2[(~s & -~s).bit_length()-1]
                    rot%=self.mod
                LEN+=1
            else:
                p=1<<(h-LEN-2)
                rot=1
                imag=self.root[2]
                for s in range(1<<LEN):
                    rot2=(rot*rot)%self.mod
                    rot3=(rot2*rot)%self.mod
                    offset=s<<(h-LEN)
                    for i in range(p):
                        a0=a[i+offset]
                        a1=a[i+offset+p]*rot
                        a2=a[i+offset+2*p]*rot2
                        a3=a[i+offset+3*p]*rot3
                        a1na3imag=(a1-a3)%self.mod*imag
                        a[i+offset]=(a0+a2+a1+a3)%self.mod
                        a[i+offset+p]=(a0+a2-a1-a3)%self.mod
                        a[i+offset+2*p]=(a0-a2+a1na3imag)%self.mod
                        a[i+offset+3*p]=(a0-a2-a1na3imag)%self.mod
                    rot*=self.rate3[(~s & -~s).bit_length()-1]
                    rot%=self.mod
                LEN+=2
                
    def butterfly_inv(self,a):
        n=len(a)
        h=(n-1).bit_length()
        LEN=h
        while(LEN):
            if (LEN==1):
                p=1<<(h-LEN)
                irot=1
                for s in range(1<<(LEN-1)):
                    offset=s<<(h-LEN+1)
                    for i in range(p):
                        l=a[i+offset]
                        r=a[i+offset+p]
                        a[i+offset]=(l+r)%self.mod
                        a[i+offset+p]=(l-r)*irot%self.mod
                    irot*=self.irate2[(~s & -~s).bit_length()-1]
                    irot%=self.mod
                LEN-=1
            else:
                p=1<<(h-LEN)
                irot=1
                iimag=self.iroot[2]
                for s in range(1<<(LEN-2)):
                    irot2=(irot*irot)%self.mod
                    irot3=(irot*irot2)%self.mod
                    offset=s<<(h-LEN+2)
                    for i in range(p):
                        a0=a[i+offset]
                        a1=a[i+offset+p]
                        a2=a[i+offset+2*p]
                        a3=a[i+offset+3*p]
                        a2na3iimag=(a2-a3)*iimag%self.mod
                        a[i+offset]=(a0+a1+a2+a3)%self.mod
                        a[i+offset+p]=(a0-a1+a2na3iimag)*irot%self.mod
                        a[i+offset+2*p]=(a0+a1-a2-a3)*irot2%self.mod
                        a[i+offset+3*p]=(a0-a1-a2na3iimag)*irot3%self.mod
                    irot*=self.irate3[(~s & -~s).bit_length()-1]
                    irot%=self.mod
                LEN-=2
    def convolution(self,a,b):
        n=len(a);m=len(b)
        if not(a) or not(b):
            return []
        if min(n,m)<=40:
            res=[0]*(n+m-1)
            for i in range(n):
                for j in range(m):
                    res[i+j]+=a[i]*b[j]
                    res[i+j]%=self.mod
            return res
        z=1<<((n+m-2).bit_length())
        a=a+[0]*(z-n)
        b=b+[0]*(z-m)
        self.butterfly(a)
        self.butterfly(b)
        c=[(a[i]*b[i])%self.mod for i in range(z)]
        self.butterfly_inv(c)
        iz=pow(z,self.mod-2,self.mod)
        for i in range(n+m-1):
            c[i]=(c[i]*iz)%self.mod
        return c[:n+m-1]

mod=998244353
fft=FFT(mod)


def bin(a,b,f,rf):
    if a<0 or b<0 or a<b:
        return 0
    return f[a]*rf[b]%mod*rf[a-b]%mod

def main():  
    n,m=read_values()
    c={}
    for _ in range(m):
        l,r=read_values()
        c[r-l+1]=c.get(r-l+1,0)+1
    if n%2:
        print(0)
        return
    f=[1]*(n+1)
    rf=[1]*(n+1)
    r=[1]*(n+1)
    for i in range(n):
        f[i+1]=f[i]*(i+1)%mod
        rf[i+1]=pow(f[i+1],-1,mod)
        r[i+1]=pow(i+1,-1,mod)
    
    dps=[[1]]
    for k,v in c.items():
        if k%2==1 or v==0:
            continue
        mul=-bin(k,k//2,f,rf)*r[k//2+1]%mod
        base=1
        add=[0]*((v+1)*(k//2))
        for i in range(v + 1):
            add[i*k//2]=bin(v,i,f,rf)*base%mod
            base=mul*base%mod
        dps.append(add)
    
    while len(dps)>1:
        ndps=[]
        for i in range(len(dps)//2):
            ndps.append(fft.convolution(dps[i*2],dps[i*2+1]))
        if len(dps)%2:
            ndps.append(dps[-1])
        dps=ndps
            
    ans=0
    for i in range(len(dps[0])):
        ans+=dps[0][i]*bin(n-i*2,n//2-i,f,rf)*r[n//2-i+1]%mod
        ans%=mod
    print(ans)
    
if __name__ == "__main__":
    main()
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