#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (998244353U) #define MINT_W (32U) #define MINT_R (301989884U) #define MINT_RR (932051910U) #define MINT_MDNINV (998244351U) #define MD_PRIMITIVE_ROOT (3U) #define PI 3.14159265358979323846 void *wmem; char memarr[96000000]; template inline S max_L(S a,T b){ return a>=b?a:b; } template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } struct Mint{ unsigned val; Mint(){ val=0; } Mint(int a){ val = mulR(a); } Mint(unsigned a){ val = mulR(a); } Mint(long long a){ val = mulR(a); } Mint(unsigned long long a){ val = mulR(a); } inline unsigned mulR(unsigned a){ return (unsigned long long)a*MINT_R%MD; } inline unsigned mulR(int a){ if(a < 0){ a = a%((int)MD)+(int)MD; } return mulR((unsigned)a); } inline unsigned mulR(unsigned long long a){ return mulR((unsigned)(a%MD)); } inline unsigned mulR(long long a){ a %= MD; if(a < 0){ a += MD; } return mulR((unsigned)a); } inline unsigned reduce(unsigned T){ unsigned m = T * MINT_MDNINV; unsigned t = (unsigned)((T + (unsigned long long)m*MD) >> MINT_W); if(t >= MD){ t -= MD; } return t; } inline unsigned reduce(unsigned long long T){ unsigned m = (unsigned)T * MINT_MDNINV; unsigned t = (unsigned)((T + (unsigned long long)m*MD) >> MINT_W); if(t >= MD){ t -= MD; } return t; } inline unsigned get(){ return reduce(val); } inline Mint &operator+=(Mint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Mint &operator-=(Mint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Mint &operator*=(Mint a){ val = reduce((unsigned long long)val*a.val); return *this; } inline Mint &operator/=(Mint a){ return *this *= a.inverse(); } inline Mint operator+(Mint a){ return Mint(*this)+=a; } inline Mint operator-(Mint a){ return Mint(*this)-=a; } inline Mint operator*(Mint a){ return Mint(*this)*=a; } inline Mint operator/(Mint a){ return Mint(*this)/=a; } inline Mint operator+(int a){ return Mint(*this)+=Mint(a); } inline Mint operator-(int a){ return Mint(*this)-=Mint(a); } inline Mint operator*(int a){ return Mint(*this)*=Mint(a); } inline Mint operator/(int a){ return Mint(*this)/=Mint(a); } inline Mint operator+(long long a){ return Mint(*this)+=Mint(a); } inline Mint operator-(long long a){ return Mint(*this)-=Mint(a); } inline Mint operator*(long long a){ return Mint(*this)*=Mint(a); } inline Mint operator/(long long a){ return Mint(*this)/=Mint(a); } inline Mint operator-(void){ Mint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Mint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Mint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = (unsigned long long)u*MINT_RR % MD; return res; } inline Mint pw(unsigned long long b){ Mint a(*this); Mint res; res.val = MINT_R; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return mulR(a)==val; } inline bool operator!=(int a){ return mulR(a)!=val; } } ; inline Mint operator+(int a, Mint b){ return Mint(a)+=b; } inline Mint operator-(int a, Mint b){ return Mint(a)-=b; } inline Mint operator*(int a, Mint b){ return Mint(a)*=b; } inline Mint operator/(int a, Mint b){ return Mint(a)/=b; } inline Mint operator+(long long a, Mint b){ return Mint(a)+=b; } inline Mint operator-(long long a, Mint b){ return Mint(a)-=b; } inline Mint operator*(long long a, Mint b){ return Mint(a)*=b; } inline Mint operator/(long long a, Mint b){ return Mint(a)/=b; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } inline void wt_L(char a){ putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ putchar_unlocked('-'); } while(s--){ putchar_unlocked(f[s]+'0'); } } template inline int isPrime_L(T n){ T i; if(n<=1){ return 0; } if(n<=3){ return 1; } if(n%2==0){ return 0; } for(i=3;i*i<=n;i+=2){ if(n%i==0){ return 0; } } return 1; } template int Factor_L(T N, T fac[], int fs[]){ T i; int sz = 0; if(N%2==0){ fac[sz] = 2; fs[sz] = 1; N /= 2; while(N%2==0){ N /= 2; fs[sz]++; } sz++; } for(i=3;i*i<=N;i+=2){ if(N%i==0){ fac[sz] = i; fs[sz] = 1; N /= i; while(N%i==0){ N /= i; fs[sz]++; } sz++; } } if(N > 1){ fac[sz] = N; fs[sz] = 1; sz++; } return sz; } template int Divisor_L(T N, T res[], void *mem = wmem){ int i; int j; int k; int s; int sz = 0; T *fc; int *fs; int fsz; walloc1d(&fc, 100, &mem); walloc1d(&fs, 100, &mem); fsz =Factor_L(N, fc, fs); res[sz++] = 1; for(i=(0);i<(fsz);i++){ s = sz; k = s * fs[i]; for(j=(0);j<(k);j++){ res[sz++] = res[j] * fc[i]; } } sort(res, res+sz); return sz; } unsigned long long powmod(unsigned long long a, unsigned long long b, unsigned long long m){ unsigned long long r = 1; while(b){ if(b&1){ r = r * a % m; } b>>=1; a = a * a % m; } return r; } long long primitiveRoot(long long p, void *mem = wmem){ int ys; long long *y; long long r; if(!isPrime_L(p)){ return -1; } walloc1d(&y, 100000, &mem); ys =Divisor_L(p-1, y, mem); for(r=(1);r<(p);r++){ int i; for(i=(0);i<(ys-1);i++){ if(powmod(r,y[i],p) == 1){ goto OC5CYxKD; } } return r; OC5CYxKD:; } return -1; } struct fft_pnt{ double x; double y; fft_pnt(void){ } fft_pnt(double a, double b){ x = a; y = b; } void set(double a, double b){ x = a; y = b; } fft_pnt& operator+=(fft_pnt a){ x+=a.x; y+=a.y; return *this; } fft_pnt& operator-=(fft_pnt a){ x-=a.x; y-=a.y; return *this; } fft_pnt& operator*=(fft_pnt a){ fft_pnt p = *this; x = p.x*a.x-p.y*a.y; y = p.x*a.y+p.y*a.x; return *this; } fft_pnt operator+(fft_pnt a){ return fft_pnt(*this) += a; } fft_pnt operator-(fft_pnt a){ return fft_pnt(*this) -= a; } fft_pnt operator*(fft_pnt a){ return fft_pnt(*this) *= a; } } ; void fft_L(int n, fft_pnt x[], void *mem){ int i; int j; int n1; int n2; int n3; int step = 1; double theta = 2*PI / n; double tmp; fft_pnt w1; fft_pnt w2; fft_pnt w3; fft_pnt a; fft_pnt b; fft_pnt c; fft_pnt d; fft_pnt aa; fft_pnt bb; fft_pnt cc; fft_pnt dd; fft_pnt *y = (fft_pnt*)mem; while(n > 2){ n1 = n / 4; n2 = n1 + n1; n3 = n1 + n2; for(i=(0);i<(n1);i++){ w1 = fft_pnt(cos(i*theta),-sin(i*theta)); w2 = w1*w1; w3 = w1*w2; for(j=(0);j<(step);j++){ a = x[j+step*i]; b = x[j+step*(i+n1)]; c = x[j+step*(i+n2)]; d = x[j+step*(i+n3)]; aa = a + c; bb = a - c; cc = b + d; dd = b - d; tmp = dd.y; dd.y = dd.x; dd.x = -tmp; y[j+step*(4*i )] = aa + cc; y[j+step*(4*i+1)] = w1*(bb - dd); y[j+step*(4*i+2)] = w2*(aa - cc); y[j+step*(4*i+3)] = w3*(bb + dd); } } n /= 4; step *= 4; theta *= 4; swap(x,y); } if(n==2){ for(i=(0);i<(step);i++){ y[i] = x[i] + x[i+step]; y[i+step] = x[i] - x[i+step]; } n /= 2; step *= 2; theta *= 2; swap(x,y); } for(i=(0);i<(step);i++){ y[i] = x[i]; } } void fftinv_L(int n, fft_pnt x[], void *mem){ int i; int j; int n1; int n2; int n3; int step = 1; double theta = 2*PI / n; double tmp; fft_pnt w1; fft_pnt w2; fft_pnt w3; fft_pnt a; fft_pnt b; fft_pnt c; fft_pnt d; fft_pnt aa; fft_pnt bb; fft_pnt cc; fft_pnt dd; fft_pnt *y = (fft_pnt*)mem; while(n > 2){ n1 = n / 4; n2 = n1 + n1; n3 = n1 + n2; for(i=(0);i<(n1);i++){ w1 = fft_pnt(cos(i*theta),sin(i*theta)); w2 = w1*w1; w3 = w1*w2; for(j=(0);j<(step);j++){ a = x[j+step*i]; b = x[j+step*(i+n1)]; c = x[j+step*(i+n2)]; d = x[j+step*(i+n3)]; aa = a + c; bb = a - c; cc = b + d; dd = b - d; tmp = dd.y; dd.y = dd.x; dd.x = -tmp; y[j+step*(4*i )] = aa + cc; y[j+step*(4*i+1)] = w1*(bb + dd); y[j+step*(4*i+2)] = w2*(aa - cc); y[j+step*(4*i+3)] = w3*(bb - dd); } } n /= 4; step *= 4; theta *= 4; swap(x,y); } if(n==2){ for(i=(0);i<(step);i++){ y[i] = x[i] + x[i+step]; y[i+step] = x[i] - x[i+step]; } n /= 2; step *= 2; theta *= 2; swap(x,y); } for(i=(0);i<(step);i++){ y[i] = x[i]; } } void convolution_L(double A[], int As, double B[], int Bs, double res[], int Rs, void *mem = wmem){ int i; int n; int n2; double mul; fft_pnt *a; fft_pnt *b; n =max_L(As+Bs, Rs); for(n2=1;n2 2){ n1 = n / 4; n2 = n1 + n1; n3 = n1 + n2; w1.val = MINT_R; for(i=(0);i<(n1);i++){ w2 = w1*w1; w3 = w1*w2; for(j=(0);j<(step);j++){ a = x[j+step*i]; b = x[j+step*(i+n1)]; c = x[j+step*(i+n2)]; d = x[j+step*(i+n3)]; aa = a + c; bb = a - c; cc = b + d; dd = (b - d) * tmp; y[j+step*(4*i )] = aa + cc; y[j+step*(4*i+1)] = w1*(bb - dd); y[j+step*(4*i+2)] = w2*(aa - cc); y[j+step*(4*i+3)] = w3*(bb + dd); } w1 *= root; } n /= 4; step *= 4; root *= root; root *= root; swap(x,y); } if(n==2){ for(i=(0);i<(step);i++){ y[i] = x[i] + x[i+step]; y[i+step] = x[i] - x[i+step]; } n /= 2; step *= 2; root *= root; swap(x,y); } for(i=(0);i<(step);i++){ y[i] = x[i]; } } void fftinv_L(int n, Mint x[], Mint root, void *mem){ int i; int j; int n1; int n2; int n3; int step = 1; Mint w1; Mint w2; Mint w3; Mint a; Mint b; Mint c; Mint d; Mint aa; Mint bb; Mint cc; Mint dd; Mint tmp; Mint *y; walloc1d(&y, n, &mem); root = root.inverse(); tmp = root.pw((MD-1)/4); root = root.pw((MD-1)/n); while(n > 2){ n1 = n / 4; n2 = n1 + n1; n3 = n1 + n2; w1.val = MINT_R; for(i=(0);i<(n1);i++){ w2 = w1*w1; w3 = w1*w2; for(j=(0);j<(step);j++){ a = x[j+step*i]; b = x[j+step*(i+n1)]; c = x[j+step*(i+n2)]; d = x[j+step*(i+n3)]; aa = a + c; bb = a - c; cc = b + d; dd = (b - d) * tmp; y[j+step*(4*i )] = aa + cc; y[j+step*(4*i+1)] = w1*(bb + dd); y[j+step*(4*i+2)] = w2*(aa - cc); y[j+step*(4*i+3)] = w3*(bb - dd); } w1 *= root; } n /= 4; step *= 4; root *= root; root *= root; swap(x,y); } if(n==2){ for(i=(0);i<(step);i++){ y[i] = x[i] + x[i+step]; y[i+step] = x[i] - x[i+step]; } n /= 2; step *= 2; root *= root; swap(x,y); } for(i=(0);i<(step);i++){ y[i] = x[i]; } } void convolution_L(Mint A[], int As, Mint B[], int Bs, Mint res[], int Rs, Mint root = MD_PRIMITIVE_ROOT, void *mem = wmem){ int i; int n; int n2; Mint *a; Mint *b; Mint r; n =max_L(As+Bs, Rs); for(n2=1;n2