
//-------------------------------------------------------------
// Modulo Arithmetics
//
// Verified by
//   - TCO10 R3 LV3
//-------------------------------------------------------------

static const int MODVAL = 1000000007; // op/ depends on primarity of the MODVAL
struct mint
{
	int val;
	mint():val(0){}
	mint(int x):val(x%MODVAL) {}
	mint(LL  x):val(x%MODVAL) {}
};

mint operator+(mint x, mint y) { return x.val+y.val; }
mint operator-(mint x, mint y) { return x.val-y.val+MODVAL; }
mint operator*(mint x, mint y) { return LL(x.val)*y.val; }
mint POW(mint x, int e) {
	mint v = 1;
	for(;e;x=x*x,e>>=1)
		if(e&1)
			v=v*x;
	return v;
}
mint operator/(mint x, mint y) { return x * POW(y, MODVAL-2); }

vector<mint> FAC_(1,1);
void FAC_INIT(int n) { for(int i=1; i<=n; ++i) FAC_.push_back( FAC_.back()*i ); }
mint FAC(mint x)       { return FAC_[x.val]; }
mint C(mint n, mint k) { return k.val<0 || n.val<k.val ? 0 : FAC(n) / (FAC(k) * FAC(n-k)); }

/*
// MODVAL must be a prime!!
LL GSS(LL k, LL b, LL e) // k^b + k^b+1 + ... + k^e
{
	if( b >  e ) return 0;
	if( k <= 1 ) return k*(e-b+1);
	return DIV(SUB(POW(k, e+1), POW(k,b)), k-1);
}

LL Cpascal(LL n, LL k)
{
	vector< vector<LL> > c(n+1, vector<LL>(k+1));
	for(LL nn=1; nn<=n; ++nn)
		for(LL kk=0; kk<=min(nn,k); ++kk)
			c[nn][kk] = kk==0 || kk==nn ? 1 : ADD(c[nn-1][kk-1], c[nn-1][kk]);
	return c[n][k];
}

vector< vector<LL> > MATMUL(vector< vector<LL> >& a, vector< vector<LL> >& b)
{
   int N = a.size();
   vector< vector<LL> > c(N, vector<LL>(N));
   for(int i=0; i<N; ++i)
   for(int j=0; j<N; ++j)
   for(int k=0; k<N; ++k)
      c[i][j] = ADD(c[i][j], MUL(a[i][k],b[k][j]));
   return c;
}

// works for non-prime MODVAL
LL GEO(LL x_, LL e) // x^0 + x^1 + ... + x^e-1
{
   vector< vector<LL> > v(2, vector<LL>(2));
   vector< vector<LL> > x(2, vector<LL>(2));
   v[0][0] = v[1][1] = 1;
   x[0][0] = x_; x[0][1] = 0;
   x[1][0] = 1 ; x[1][1] = 1;
   for(;e;x=MATMUL(x,x),e>>=1)
      if(e&1)
         v = MATMUL(v, x);
   return v[1][0];
}

// works for non-prime MODVAL
LL HYP(LL x_, LL e) // e x^0 + (e-1) x^1 + ... + 1 x^e-1 = GEO(x,1)+GEO(x,2)+...+GEO(x,e)
{
   vector< vector<LL> > v(3, vector<LL>(3));
   vector< vector<LL> > x(3, vector<LL>(3));
   v[0][0] = v[1][1] = v[2][2] = 1;
   x[0][0] = x_; x[0][1] = 0; x[0][2] = 0;
   x[1][0] = 1 ; x[1][1] = 1; x[1][2] = 0;
   x[2][0] = 0 ; x[2][1] = 1; x[2][2] = 1;
   e++;
   for(;e;x=MATMUL(x,x),e>>=1)
      if(e&1)
         v = MATMUL(v, x);
   return v[2][0];
}
*/
