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Karatsuba.cpp
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Karatsuba.cpp
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#include<bits/stdc++.h>
typedef long long LL;
using namespace std;
#define MP Make_pair
#define PB push_back
#define all(v) (v).begin(),(v).end()
#define endl '\n'
LL M = (LL)1e9+7;
const LL N = 10005;
//polynoMials are taken as a0 + a1x + a2x^2...
LL mem[N * 60];
LL a[N],b[N],ret[N];
LL Mid;
void Mult(LL *A, LL *B, LL *C, LL n)
{
if (n <= 64) {
// cout << "YOa" << C[1] << endl;
for (LL i=0; i<n; i++)
for (LL j=0; j<n; j++) (C[i+j] += A[i] * B[j]) %= M;
// cout << "YOb" << C[1] << endl;
return;
}
LL base = Mid;
Mid += n * 3;
fill(mem+base, mem+Mid, 0);
LL hn = n/2;
Mult(A, B, mem+base, hn);
Mult(A+hn, B+hn, mem+base+n, hn);
LL bb = Mid;
Mid += n;
for (LL i=0; i<hn; i++) {
mem[bb+i] = (A[i] + A[hn+i]);
if (mem[bb+i] >= M) mem[bb+i] -= M;
}
for (LL i=0; i<hn; i++) {
mem[bb+hn+i] = (B[i] + B[hn+i]);
if (mem[bb+hn+i] >= M) mem[bb+hn+i] -= M;
}
Mult(mem+bb, mem+bb+hn, mem+base+n+n, hn);
for (LL i=0; i<n; i++) {
C[i] += mem[base+i];
C[i+hn] += mem[base+n+n+i] - mem[base+i] - mem[base+n+i];
C[i+n] += mem[base+n+i];
}
for (LL i=0; i<2*n; i++) {
if (C[i] >= M) C[i] -= M;
if (C[i] < 0) C[i] += M;
if (C[i] < 0) C[i] += M;
}
Mid -= 4 * n;
}
LL fac[N];
int main()
{
ios_base::sync_with_stdio(0);
cout.precision(15);
cout.setf(ios::fixed) ;
fac[0] = 1;
LL t;
cin >> t;
for(LL xx=1;xx<=t;xx++)
{
//using FFT
LL n;
cin >> n >> M;
memset(a,0,sizeof(a));
memset(b,0,sizeof(b));
memset(ret,0,sizeof(ret));
fac[0] = 1;
b[1] = 1;
for(LL i=1;i<N;i++)
fac[i] = (fac[i-1]*i)%M;
for(LL i=2;i<=n;i++)
{
b[i] = fac[i];
for(LL j=1;j<i;j++)
b[i] = (b[i] - fac[i-j]*b[j]%M + M)%M;
}
for(LL i=0;i<=n;i++) a[0] = 0;
a[0] = 1;
LL ans = 0;
for(LL i=1;i<=n;i++)
{
memset(ret,0,sizeof(ret));
Mult(a,b,ret,n+2);
for(LL i=0;i<=n;i++)
a[i] = (ret[i]%M)%M;
ans = (ans + i*i*a[n])%M;
}
cout <<"Case #"<<xx<<": "<<ans << endl;
}
}