思路和任意模数FFT模板都来自

看了一晚上那篇《再探快速傅里叶变换》还是懵得不行，可能水平还没到- -

只能先存个模板了，这题单模数NTT跑了5.9s，没敢写三模数NTT，可能姿势太差了...

具体推导大概这样就可以了：

/*HDU 6088 - Rikka with Rock-paper-scissors [ 任意模数FFT,数论 ]  |  2017 Multi-University Training Contest 5题意：	计算 3^n * ∑ [0<=i+j<=n] C(n, i) * C(n-i, j) * GCD(i,j)	N <= 1e5分析：	利用 n = ∑ [d|n] φ(d)	化得：		3^n * ∑[1<=d<=n] d ∑ [0<=i+j<=n/d] C(n,i*d) * C(n-i*d, j*d)	之后枚举 d  （以下略写 *d ）		C(n,i*d) * C(n-i*d, j*d)		= n! * 1/(i!) * 1/(j!) * 1/(n-i-j)!			维护 f(i) = 1/i! 的卷积 g(k) = ∑ [i+j == k] * f(i) * f(j)		原式 = ∑[1<=i<=m] n! * g(k) * 1/(n-k)!	由于 gcd(0, 0) == 0	所以特判卷积的 g(0) 项不用加上*/#include 
     
      using namespace std;#define MOD mod#define upmo(a,b) (((a)=((a)+(b))%MOD)<0?(a)+=MOD:(a))typedef long long LL;typedef double db;const int N = 1e5+5;int t, n;LL inv[N], F[N], Finv[N], phi[N];LL MOD;namespace FFT_MO{    const int FFT_MAXN = 1<<18;    const db PI = 4*atan(1.0);    struct cp    {        db a, b;        cp(db a_ = 0, db b_ = 0) {            a = a_, b = b_;        }        cp operator + (const cp& rhs) const {            return cp(a+rhs.a, b+rhs.b);        }        cp operator - (const cp& rhs) const {            return cp(a-rhs.a, b-rhs.b);        }        cp operator * (const cp& rhs) const {            return cp(a*rhs.a-b*rhs.b, a*rhs.b + b*rhs.a);        }        cp operator !() const{            return cp(a, -b);        }    }nw[FFT_MAXN+1], f[FFT_MAXN], g[FFT_MAXN], t[FFT_MAXN];    int bitrev[FFT_MAXN];    void fft_init()    {        int L = 0; while ((1<
      
       >1]>>1 | ((i&1)<<(L-1));        for (int i = 0; i <= FFT_MAXN; i++)            nw[i] = cp((db)cosl(2*PI/FFT_MAXN*i), (db)sinl(2*PI/FFT_MAXN*i));    }    void dft(cp *a, int n, int flag = 1)    {        int d = 0; while ((1<
       
        >d))            swap(a[i], a[bitrev[i]>>d]);        for (int l = 2; l <= n; l <<= 1)        {            int del = FFT_MAXN/l*flag;            for (int i = 0; i < n; i += l)            {                cp *le = a+i, *ri = a+i+(l>>1);                cp *w = flag==1 ? nw : nw+FFT_MAXN;                for (int k = 0; k < (l>>1); k++)                {                    cp ne = *ri * *w;                    *ri = *le - ne, *le = *le+ne;                    le++, ri++, w += del;                }            }        }        if (flag != 1) for (int i = 0; i < n; i++) a[i].a /= n, a[i].b /= n;    }    void convo(LL *a, int n, LL *b, int m, LL *c)    {        for (int i = 0; i <= n+m; i++) c[i] = 0;        int N = 2; while (N <= n+m) N <<= 1;        for (int i = 0; i < N; i++)        {            LL aa = i <= n ? a[i] : 0, bb = i <= m ? b[i] : 0;            aa %= MOD, bb %= MOD;            f[i] = cp(db(aa>>15), db(aa&32767));            g[i] = cp(db(bb>>15), db(bb&32767));        }        dft(f, N), dft(g, N);        for (int i = 0; i < N; i++)        {            int j = i ? N-i : 0;            t[i] = ((f[i]+!f[j])*(!g[j]-g[i]) + (!f[j]-f[i])*(g[i]+!g[j])) * cp(0, 0.25);        }        dft(t, N, -1);        for (int i = 0; i <= n+m; i++) upmo(c[i], (LL(t[i].a+0.5))%MOD<<15);        for (int i = 0; i < N; i++)        {            int j = i? N-i : 0;            t[i] = (!f[j]-f[i])*(!g[j]-g[i])*cp(-0.25,0) + cp(0,0.25)*(f[i]+!f[j])*(g[i]+!g[j]);        }        dft(t, N, -1);        for (int i = 0; i <= n+m; i++)            upmo(c[i], LL(t[i].a+0.5)+(LL(t[i].b+0.5)%MOD<<30));    }}LL a[1<<18|1], b[1<<18|1], c[1<<18|1];LL PowMod(LL a, LL m){    a %= MOD;    LL ret = 1;    while (m) {        if (m&1) ret = ret * a % MOD;        m >>= 1;        a = a*a % MOD;    }    return ret;}void GetEuler(){    memset(phi, 0, sizeof(phi));    phi[1] = 1;    for (int i = 2; i < N; i++)        if (!phi[i])            for (int j = i; j < N; j += i)            {                if (!phi[j]) phi[j] = j;                phi[j] = phi[j] / i * (i-1);            }}void init(int n) {    inv[1] = 1;    for (int i = 2; i <= n; i++)        inv[i] = (MOD - MOD/i) *inv[MOD % i] % MOD;    F[0] = Finv[0] = 1;    for (int i = 1; i <= n; i++) {        F[i] = F[i-1] * i % MOD;        Finv[i] = Finv[i-1] * inv[i] % MOD;    }}int main(){    GetEuler();    scanf("%d", &t);    while (t--)    {        scanf("%d%lld", &n, &MOD);        init(n);        FFT_MO::fft_init();        LL ans = 0;        for (int d = 1; d <= n; d++)        {            int m = n/d;            for (int i = 0; i <= m; i++) b[i] = a[i] = Finv[i*d];            FFT_MO::convo(a, m, b, m, c);            for (int i = 0; i <= m; i++) c[i] = c[i] * Finv[n-i*d] % MOD;            LL sum = 0;            for (int i = 1; i <= m; i++) sum = (sum + c[i]) % MOD;            ans = (ans + sum * phi[d]) % MOD;        }        ans = ans * F[n] % MOD * PowMod(3, n) % MOD;        printf("%lld\n", ans);    }}