4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: //------------------------------------------------------------- 4fd800b3a8 2011-02-23 kinaba: // Modulo Arithmetics 4fd800b3a8 2011-02-23 kinaba: // 4fd800b3a8 2011-02-23 kinaba: // Verified by 4fd800b3a8 2011-02-23 kinaba: // - TCO10 R3 LV3 4fd800b3a8 2011-02-23 kinaba: //------------------------------------------------------------- 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: static const int MODVAL = 1000000007; // op/ depends on primarity of the MODVAL 4fd800b3a8 2011-02-23 kinaba: struct mint 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: int val; 4fd800b3a8 2011-02-23 kinaba: mint():val(0){} 4fd800b3a8 2011-02-23 kinaba: mint(int x):val(x%MODVAL) {} 4fd800b3a8 2011-02-23 kinaba: mint(LL x):val(x%MODVAL) {} 4fd800b3a8 2011-02-23 kinaba: }; 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: mint operator+(mint x, mint y) { return x.val+y.val; } 4fd800b3a8 2011-02-23 kinaba: mint operator-(mint x, mint y) { return x.val-y.val+MODVAL; } 4fd800b3a8 2011-02-23 kinaba: mint operator*(mint x, mint y) { return LL(x.val)*y.val; } 4fd800b3a8 2011-02-23 kinaba: mint POW(mint x, int e) { 4fd800b3a8 2011-02-23 kinaba: mint v = 1; 4fd800b3a8 2011-02-23 kinaba: for(;e;x=x*x,e>>=1) 4fd800b3a8 2011-02-23 kinaba: if(e&1) 4fd800b3a8 2011-02-23 kinaba: v=v*x; 4fd800b3a8 2011-02-23 kinaba: return v; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: mint operator/(mint x, mint y) { return x * POW(y, MODVAL-2); } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: vector<mint> FAC_(1,1); 4fd800b3a8 2011-02-23 kinaba: void FAC_INIT(int n) { for(int i=1; i<=n; ++i) FAC_.push_back( FAC_.back()*i ); } 4fd800b3a8 2011-02-23 kinaba: mint FAC(mint x) { return FAC_[x.val]; } 4fd800b3a8 2011-02-23 kinaba: mint C(mint n, mint k) { return k.val<0 || n.val<k.val ? 0 : FAC(n) / (FAC(k) * FAC(n-k)); } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: /* 4fd800b3a8 2011-02-23 kinaba: // MODVAL must be a prime!! 4fd800b3a8 2011-02-23 kinaba: LL GSS(LL k, LL b, LL e) // k^b + k^b+1 + ... + k^e 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: if( b > e ) return 0; 4fd800b3a8 2011-02-23 kinaba: if( k <= 1 ) return k*(e-b+1); 4fd800b3a8 2011-02-23 kinaba: return DIV(SUB(POW(k, e+1), POW(k,b)), k-1); 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL Cpascal(LL n, LL k) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > c(n+1, vector<LL>(k+1)); 4fd800b3a8 2011-02-23 kinaba: for(LL nn=1; nn<=n; ++nn) 4fd800b3a8 2011-02-23 kinaba: for(LL kk=0; kk<=min(nn,k); ++kk) 4fd800b3a8 2011-02-23 kinaba: c[nn][kk] = kk==0 || kk==nn ? 1 : ADD(c[nn-1][kk-1], c[nn-1][kk]); 4fd800b3a8 2011-02-23 kinaba: return c[n][k]; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > MATMUL(vector< vector<LL> >& a, vector< vector<LL> >& b) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: int N = a.size(); 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > c(N, vector<LL>(N)); 4fd800b3a8 2011-02-23 kinaba: for(int i=0; i<N; ++i) 4fd800b3a8 2011-02-23 kinaba: for(int j=0; j<N; ++j) 4fd800b3a8 2011-02-23 kinaba: for(int k=0; k<N; ++k) 4fd800b3a8 2011-02-23 kinaba: c[i][j] = ADD(c[i][j], MUL(a[i][k],b[k][j])); 4fd800b3a8 2011-02-23 kinaba: return c; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: // works for non-prime MODVAL 4fd800b3a8 2011-02-23 kinaba: LL GEO(LL x_, LL e) // x^0 + x^1 + ... + x^e-1 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > v(2, vector<LL>(2)); 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > x(2, vector<LL>(2)); 4fd800b3a8 2011-02-23 kinaba: v[0][0] = v[1][1] = 1; 4fd800b3a8 2011-02-23 kinaba: x[0][0] = x_; x[0][1] = 0; 4fd800b3a8 2011-02-23 kinaba: x[1][0] = 1 ; x[1][1] = 1; 4fd800b3a8 2011-02-23 kinaba: for(;e;x=MATMUL(x,x),e>>=1) 4fd800b3a8 2011-02-23 kinaba: if(e&1) 4fd800b3a8 2011-02-23 kinaba: v = MATMUL(v, x); 4fd800b3a8 2011-02-23 kinaba: return v[1][0]; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: // works for non-prime MODVAL 4fd800b3a8 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) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > v(3, vector<LL>(3)); 4fd800b3a8 2011-02-23 kinaba: vector< vector<LL> > x(3, vector<LL>(3)); 4fd800b3a8 2011-02-23 kinaba: v[0][0] = v[1][1] = v[2][2] = 1; 4fd800b3a8 2011-02-23 kinaba: x[0][0] = x_; x[0][1] = 0; x[0][2] = 0; 4fd800b3a8 2011-02-23 kinaba: x[1][0] = 1 ; x[1][1] = 1; x[1][2] = 0; 4fd800b3a8 2011-02-23 kinaba: x[2][0] = 0 ; x[2][1] = 1; x[2][2] = 1; 4fd800b3a8 2011-02-23 kinaba: e++; 4fd800b3a8 2011-02-23 kinaba: for(;e;x=MATMUL(x,x),e>>=1) 4fd800b3a8 2011-02-23 kinaba: if(e&1) 4fd800b3a8 2011-02-23 kinaba: v = MATMUL(v, x); 4fd800b3a8 2011-02-23 kinaba: return v[2][0]; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: */