23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: //-------------------------------------------------------------
23dfcca431 2011-02-23        kinaba: // Modulo Arithmetics
23dfcca431 2011-02-23        kinaba: //
23dfcca431 2011-02-23        kinaba: // Verified by
23dfcca431 2011-02-23        kinaba: //   - SRM 397 Div1 LV2
23dfcca431 2011-02-23        kinaba: //   - SRM 428 Div1 LV2
23dfcca431 2011-02-23        kinaba: //   - CodeCraft 2010 CNTINT DRAW
23dfcca431 2011-02-23        kinaba: //-------------------------------------------------------------
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: static const LL MODVAL = 1000000007; // must fit in 32-bits
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: LL ADD(LL x, LL y) { return (x+y)%MODVAL; }
23dfcca431 2011-02-23        kinaba: LL SUB(LL x, LL y) { return (x-y+MODVAL)%MODVAL; }
23dfcca431 2011-02-23        kinaba: LL MUL(LL x, LL y) { return (x*y)%MODVAL; }
23dfcca431 2011-02-23        kinaba: LL POW(LL x, LL e) {
23dfcca431 2011-02-23        kinaba: 	LL v = 1;
23dfcca431 2011-02-23        kinaba: 	for(;e;x=MUL(x,x),e>>=1)
23dfcca431 2011-02-23        kinaba: 		if(e&1)
23dfcca431 2011-02-23        kinaba: 			v = MUL(v, x);
23dfcca431 2011-02-23        kinaba: 	return v;
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: // MODVAL must be a prime!!
23dfcca431 2011-02-23        kinaba: LL DIV(LL x, LL y) { return MUL(x, POW(y, MODVAL-2)); }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: // MODVAL must be a prime!!
23dfcca431 2011-02-23        kinaba: LL C(LL n, LL k) {
23dfcca431 2011-02-23        kinaba: 	LL v = 1;
23dfcca431 2011-02-23        kinaba: 	for(LL i=1; i<=k; ++i)
23dfcca431 2011-02-23        kinaba: 		v = DIV(MUL(v, n-i+1), i);
23dfcca431 2011-02-23        kinaba: 	return v;
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: // MODVAL must be a prime!!
23dfcca431 2011-02-23        kinaba: LL GSS(LL k, LL b, LL e) // k^b + k^b+1 + ... + k^e
23dfcca431 2011-02-23        kinaba: {
23dfcca431 2011-02-23        kinaba: 	if( b >  e ) return 0;
23dfcca431 2011-02-23        kinaba: 	if( k <= 1 ) return k*(e-b+1);
23dfcca431 2011-02-23        kinaba: 	return DIV(SUB(POW(k, e+1), POW(k,b)), k-1);
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: LL Cpascal(LL n, LL k)
23dfcca431 2011-02-23        kinaba: {
23dfcca431 2011-02-23        kinaba: 	vector< vector<LL> > c(n+1, vector<LL>(k+1));
23dfcca431 2011-02-23        kinaba: 	for(LL nn=1; nn<=n; ++nn)
23dfcca431 2011-02-23        kinaba: 		for(LL kk=0; kk<=min(nn,k); ++kk)
23dfcca431 2011-02-23        kinaba: 			c[nn][kk] = kk==0 || kk==nn ? 1 : ADD(c[nn-1][kk-1], c[nn-1][kk]);
23dfcca431 2011-02-23        kinaba: 	return c[n][k];
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: vector< vector<LL> > MATMUL(vector< vector<LL> >& a, vector< vector<LL> >& b)
23dfcca431 2011-02-23        kinaba: {
23dfcca431 2011-02-23        kinaba:    int N = a.size();
23dfcca431 2011-02-23        kinaba:    vector< vector<LL> > c(N, vector<LL>(N));
23dfcca431 2011-02-23        kinaba:    for(int i=0; i<N; ++i)
23dfcca431 2011-02-23        kinaba:    for(int j=0; j<N; ++j)
23dfcca431 2011-02-23        kinaba:    for(int k=0; k<N; ++k)
23dfcca431 2011-02-23        kinaba:       c[i][j] = ADD(c[i][j], MUL(a[i][k],b[k][j]));
23dfcca431 2011-02-23        kinaba:    return c;
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: // works for non-prime MODVAL
23dfcca431 2011-02-23        kinaba: LL GEO(LL x_, LL e) // x^0 + x^1 + ... + x^e-1
23dfcca431 2011-02-23        kinaba: {
23dfcca431 2011-02-23        kinaba:    vector< vector<LL> > v(2, vector<LL>(2));
23dfcca431 2011-02-23        kinaba:    vector< vector<LL> > x(2, vector<LL>(2));
23dfcca431 2011-02-23        kinaba:    v[0][0] = v[1][1] = 1;
23dfcca431 2011-02-23        kinaba:    x[0][0] = x_; x[0][1] = 0;
23dfcca431 2011-02-23        kinaba:    x[1][0] = 1 ; x[1][1] = 1;
23dfcca431 2011-02-23        kinaba:    for(;e;x=MATMUL(x,x),e>>=1)
23dfcca431 2011-02-23        kinaba:       if(e&1)
23dfcca431 2011-02-23        kinaba:          v = MATMUL(v, x);
23dfcca431 2011-02-23        kinaba:    return v[1][0];
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
23dfcca431 2011-02-23        kinaba: // works for non-prime MODVAL
23dfcca431 2011-02-23        kinaba: 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)
23dfcca431 2011-02-23        kinaba: {
23dfcca431 2011-02-23        kinaba:    vector< vector<LL> > v(3, vector<LL>(3));
23dfcca431 2011-02-23        kinaba:    vector< vector<LL> > x(3, vector<LL>(3));
23dfcca431 2011-02-23        kinaba:    v[0][0] = v[1][1] = v[2][2] = 1;
23dfcca431 2011-02-23        kinaba:    x[0][0] = x_; x[0][1] = 0; x[0][2] = 0;
23dfcca431 2011-02-23        kinaba:    x[1][0] = 1 ; x[1][1] = 1; x[1][2] = 0;
23dfcca431 2011-02-23        kinaba:    x[2][0] = 0 ; x[2][1] = 1; x[2][2] = 1;
23dfcca431 2011-02-23        kinaba:    e++;
23dfcca431 2011-02-23        kinaba:    for(;e;x=MATMUL(x,x),e>>=1)
23dfcca431 2011-02-23        kinaba:       if(e&1)
23dfcca431 2011-02-23        kinaba:          v = MATMUL(v, x);
23dfcca431 2011-02-23        kinaba:    return v[2][0];
23dfcca431 2011-02-23        kinaba: }