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template<class H, size_t SIZE>
struct SquareMatrix {
using T = typename H::T;
using ar = array<T, SIZE>;
using mat = array<ar, SIZE>;
mat A;
SquareMatrix() {
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
A[i][j] = H::zero();
}
}
}
static SquareMatrix I(){
SquareMatrix X;
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
if(i == j) X[i][j] = H::one();
else X[i][j] = H::zero();
}
}
return X;
}
friend ar operator*=(ar &x, const SquareMatrix &Y) {
ar ans;
fill(begin(ans), end(ans), mint(0));
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
H::add(ans[j], H::mul(x[i], Y[i][j]));
}
}
x.swap(ans);
return x;
}
friend ar operator*(ar x, const SquareMatrix &Y) { return x *= Y; }
inline const ar &operator[](int k) const{ return (A.at(k)); }
inline ar &operator[](int k) { return (A.at(k)); }
SquareMatrix &operator+= (const SquareMatrix &B){
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
H::add((*this)[i][j], B[i][j]);
}
}
return (*this);
}
SquareMatrix &operator-= (const SquareMatrix &B){
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
H::add((*this)[i][j], -B[i][j]);
}
}
return (*this);
}
SquareMatrix &operator*=(const SquareMatrix &B) {
SquareMatrix C{};
for (int i = 0; i < SIZE; ++i) {
for (int k = 0; k < SIZE; ++k) {
for (int j = 0; j < SIZE; ++j) {
H::add(C[i][j], H::mul((*this)[i][k], B[k][j]));
}
}
}
A.swap(C.A);
return (*this);
}
SquareMatrix pow(ll n) const {
SquareMatrix a = (*this), res = I();
while(n > 0){
if(n & 1) res *= a;
a *= a;
n >>= 1;
}
return res;
}
SquareMatrix operator+(const SquareMatrix &B) const {return SquareMatrix(*this) += B;}
SquareMatrix operator-(const SquareMatrix &B) const {return SquareMatrix(*this) -= B;}
SquareMatrix operator*(const SquareMatrix &B) const {return SquareMatrix(*this) *= B;}
};
#line 1 "math/squarematrix.cpp"
template<class H, size_t SIZE>
struct SquareMatrix {
using T = typename H::T;
using ar = array<T, SIZE>;
using mat = array<ar, SIZE>;
mat A;
SquareMatrix() {
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
A[i][j] = H::zero();
}
}
}
static SquareMatrix I(){
SquareMatrix X;
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
if(i == j) X[i][j] = H::one();
else X[i][j] = H::zero();
}
}
return X;
}
friend ar operator*=(ar &x, const SquareMatrix &Y) {
ar ans;
fill(begin(ans), end(ans), mint(0));
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
H::add(ans[j], H::mul(x[i], Y[i][j]));
}
}
x.swap(ans);
return x;
}
friend ar operator*(ar x, const SquareMatrix &Y) { return x *= Y; }
inline const ar &operator[](int k) const{ return (A.at(k)); }
inline ar &operator[](int k) { return (A.at(k)); }
SquareMatrix &operator+= (const SquareMatrix &B){
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
H::add((*this)[i][j], B[i][j]);
}
}
return (*this);
}
SquareMatrix &operator-= (const SquareMatrix &B){
for (int i = 0; i < SIZE; ++i) {
for (int j = 0; j < SIZE; ++j) {
H::add((*this)[i][j], -B[i][j]);
}
}
return (*this);
}
SquareMatrix &operator*=(const SquareMatrix &B) {
SquareMatrix C{};
for (int i = 0; i < SIZE; ++i) {
for (int k = 0; k < SIZE; ++k) {
for (int j = 0; j < SIZE; ++j) {
H::add(C[i][j], H::mul((*this)[i][k], B[k][j]));
}
}
}
A.swap(C.A);
return (*this);
}
SquareMatrix pow(ll n) const {
SquareMatrix a = (*this), res = I();
while(n > 0){
if(n & 1) res *= a;
a *= a;
n >>= 1;
}
return res;
}
SquareMatrix operator+(const SquareMatrix &B) const {return SquareMatrix(*this) += B;}
SquareMatrix operator-(const SquareMatrix &B) const {return SquareMatrix(*this) -= B;}
SquareMatrix operator*(const SquareMatrix &B) const {return SquareMatrix(*this) *= B;}
};