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: //   - TCO10 R3 LV3
7d2fe88cb2 2012-09-08        kinaba: //   - SRM 545 Div1 LV2
7d2fe88cb2 2012-09-08        kinaba: //   - SRM 554 Div1 LV3
23dfcca431 2011-02-23        kinaba: //-------------------------------------------------------------
23dfcca431 2011-02-23        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: static const unsigned MODVAL = 1000000007;
23dfcca431 2011-02-23        kinaba: struct mint
23dfcca431 2011-02-23        kinaba: {
0ea7f42c5c 2012-09-02        kinaba: 	unsigned val;
23dfcca431 2011-02-23        kinaba: 	mint():val(0){}
0ea7f42c5c 2012-09-02        kinaba: 	mint(int      x):val(x%MODVAL) {}
0ea7f42c5c 2012-09-02        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
0ea7f42c5c 2012-09-02        kinaba: 	mint(LL       x):val(x%MODVAL) {}
23dfcca431 2011-02-23        kinaba: };
068d2337c1 2011-09-18        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
068d2337c1 2011-09-18        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
068d2337c1 2011-09-18        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
068d2337c1 2011-09-18        kinaba: mint operator+(mint x, mint y) { return x+=y; }
068d2337c1 2011-09-18        kinaba: mint operator-(mint x, mint y) { return x-=y; }
068d2337c1 2011-09-18        kinaba: mint operator*(mint x, mint y) { return x*=y; }
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
0ea7f42c5c 2012-09-02        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
068d2337c1 2011-09-18        kinaba: mint operator/(mint x, mint y) { return x/=y; }
0ea7f42c5c 2012-09-02        kinaba: 
23dfcca431 2011-02-23        kinaba: vector<mint> FAC_(1,1);
068d2337c1 2011-09-18        kinaba: mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*FAC_.size() ); return FAC_[n]; }
7d2fe88cb2 2012-09-08        kinaba: 
7d2fe88cb2 2012-09-08        kinaba: // nCk :: O(log MODVAL) time, O(n) space.
068d2337c1 2011-09-18        kinaba: mint C(LL n, LL k) { return k<0 || n<k ? 0 : FAC(n) / (FAC(k) * FAC(n-k)); }
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: // nCk :: O(1) time, O(n^2) space.
0ea7f42c5c 2012-09-02        kinaba: vector< vector<mint> > CP_;
16685c1758 2012-06-07        kinaba: mint C(LL n, LL k) {
4318dd2827 2012-06-07        kinaba: 	while( CP_.size() <= n ) {
4318dd2827 2012-06-07        kinaba: 		int nn = CP_.size();
4318dd2827 2012-06-07        kinaba: 		CP_.push_back(vector<mint>(nn+1,1));
4318dd2827 2012-06-07        kinaba: 		for(int kk=1; kk<nn; ++kk)
4318dd2827 2012-06-07        kinaba: 			CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
16685c1758 2012-06-07        kinaba: 	}
16685c1758 2012-06-07        kinaba: 	return k<0 || n<k ? 0 : CP_[n][k];
23dfcca431 2011-02-23        kinaba: }
23dfcca431 2011-02-23        kinaba: 
7d2fe88cb2 2012-09-08        kinaba: // O(log MODVAL), MODVAL must be prime: k^b + k^b+1 + ... + k^e
7d2fe88cb2 2012-09-08        kinaba: mint GSS(mint k, LL b, LL e)
23dfcca431 2011-02-23        kinaba: {
7d2fe88cb2 2012-09-08        kinaba: 	if( b > e ) return 0;
7d2fe88cb2 2012-09-08        kinaba: 	if( k.val <= 1 ) return k*(e-b+1);
7d2fe88cb2 2012-09-08        kinaba: 	return (POW(k, e+1) - POW(k,b)) / (k-1);
23dfcca431 2011-02-23        kinaba: }