Fast number theory Transformation (NTT)

Today's a question, bare ntt, but I will not, so White sent 50 points.
So he came to learn about NTT.
The surface is very simple, do not bother to post, that is not the point I want to say.
The emphasis is on NTT, also called the Fast number theory transformation.
In many problems, we may encounter the polynomial multiplication problem in the mode meaning, when the traditional fast Fourier transform may not satisfy the request, this time the fast number theory transformation is useful.
Considering the realization of fast Fourier transform, using the special properties of unit complex root to reduce the operation, the cyclic convolution characteristic of DfT transform is used. So consider something that also has cyclic convolution characteristics in a modal sense.
Consider in the sense of modulo p ( p For a given prime number, meet P=C? 2 n +1 )
We make p One of the original roots for g , so analogy to the FFT, our unit root is g p? 1 n , and then other processes are analogous to the FFT.

#include <bits/stdc++.h>using namespace STD;typedef Long Longlltypedef DoubledbConst intinf=0x3f3f3f3f;intGetint () {intf=1, g=0;CharC=getchar (); while(c<' 0 '|| C>' 9 '){if(c=='-') f=-1; C=getchar ();} while(c>=' 0 '&& c<=' 9 ') g= (g<<3) + (g<<1) +c-' 0 ', C=getchar ();returnF*g;}Const intmaxn=1<< -;Const intg=7;Const intMod=950009857;intInvintw[2][MAXN];intN,m,k;intREV[MAXN];intNintCnt;ll Power (ll X,ll y) {ll res=1lL for(; y;y>>=1, x= (x*x)%mod) {if(y&1) Res=res*x%mod; }returnRes;}voidInit () { for(n=1;n<n<<1; n<<=1, cnt++); Inv=power (n,mod-2); w[0][0]=w[0][n]=w[1][0]=w[1][n]=1;intG=power (G, (mod-1)/n); for(intI=1; i<=n-1; i++) {w[0][i]= (LL) w[0][i-1]*g%mod; } for(intI=0; i<=n;i++) {w[1][i]=w[0][n-i]; } for(intI=0; i<=n;i++) {intTemp=i;intpos=0; for(intj=1; j<=cnt;j++) {pos<<=1;p OS |=temp&1; temp>>=1;    } Rev[i]=pos; }}voidFftintA[],intNintV) {inti,j,l; for(i=0; i<n;i++) {if(I>rev[i]) swap (a[i],a[rev[i]); } for(i=2; i<=n;i<<=1)    {intMid=i>>1; for(j=0; j<n;j+=i) { for(l=0; l<mid;l++) {intt= (LL) a[j+l+mid]*w[v][(n/i) *l]%mod;                A[j+l+ (mid)]= ((LL) a[j+l]-t+mod)%mod;            a[j+l]= (LL) a[j+l]+t)%mod; }        }    }}intMain () {return 0;}

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Fast number theory Transformation (NTT)