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Math.cpp
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#include <bits/stdc++.h>
using namespace std;
template<int P> struct mint
{
int v;
mint(const int x=0): v(x) {}
template<typename T> mint& operator=(const T &a) {*this=mint(a); return (*this);}
bool operator==(const mint &a) const {return v==a.v;}
mint operator+(const mint &a) const {const int r=v+a.v; return mint(r<P?r:r-P);}
mint operator-(const mint &a) const {const int r=v-a.v; return mint(r<0?r+P:r);}
mint operator-() const {return mint(P-v);}
mint operator*(const mint &a) const {return mint(1ll*v*a.v%P);}
mint& operator+=(const mint &a) {(*this)=(*this)+a; return (*this);}
mint& operator-=(const mint &a) {(*this)=(*this)-a; return (*this);}
mint& operator*=(const mint &a) {(*this)=(*this)*a; return (*this);}
mint pow(long long k) const
{
mint r=1,a=(*this);
while (k)
{
if (k&1) r*=a;
a*=a; k>>=1;
}
return r;
}
mint inv() const {return pow(P-2);}
mint operator/(const mint &a) const {return (*this)*a.inv();}
mint& operator/=(const mint &b) {(*this)=(*this)/b; return (*this);}
};
template<int P> struct Matrix
{
int n;
vector<vector<mint<P>>> v;
Matrix(int n, int d=0): n(n),v(n,vector<mint<P>>(n))
{
if (d) for (int i=0;i<n;i++) v[i][i]=d;
}
Matrix operator* (const Matrix &a) const
{
Matrix re(n);
for (int i=0;i<n;i++)
{
for (int j=0;j<n;j++)
{
for (int k=0;k<n;k++)
{
re.v[i][j]+=v[i][k]*a.v[k][j];
}
}
}
return re;
}
Matrix operator*= (const Matrix &a) {(*this)=(*this)*a; return (*this);}
mint<P> elim(Matrix &b)
{
mint<P> re=1;
Matrix a=*this;
for (int i=0;i<n;i++)
{
if (a.v[i][i].v==0)
{
for (int j=i+1;j<n;j++)
{
if (a.v[j][i].v)
{
swap(a.v[i],a.v[j]);
swap(b.v[i],b.v[j]);
re=-re;
break;
}
}
if (a.v[i][i].v==0) return 0;
}
const mint<P> x=a.v[i][i],invx=x.inv();
re*=x;
for (int j=0;j<n;j++)
{
a.v[i][j]*=invx;
b.v[i][j]*=invx;
}
for (int k=0;k<n;k++)
{
if (k==i) continue;
const mint<P> y=a.v[k][i];
for (int j=0;j<n;j++)
{
a.v[k][j]-=a.v[i][j]*y;
b.v[k][j]-=b.v[i][j]*y;
}
}
}
return re;
}
mint<P> det()
{
Matrix e(n);
return elim(e);
}
Matrix inv()
{
Matrix e(n,1);
const mint<P> d=elim(e);
if (d.v==0) return Matrix(0);
return e;
}
Matrix pow(long long k)
{
Matrix r(n,1),a=(*this);
while (k)
{
if (k&1) r*=a;
a*=a; k>>=1;
}
return r;
}
};