4fd800b3a8 2011-02-23        kinaba: #include <iostream>
4fd800b3a8 2011-02-23        kinaba: #include <sstream>
4fd800b3a8 2011-02-23        kinaba: #include <iomanip>
4fd800b3a8 2011-02-23        kinaba: #include <vector>
4fd800b3a8 2011-02-23        kinaba: #include <string>
4fd800b3a8 2011-02-23        kinaba: #include <map>
4fd800b3a8 2011-02-23        kinaba: #include <set>
4fd800b3a8 2011-02-23        kinaba: #include <algorithm>
4fd800b3a8 2011-02-23        kinaba: #include <numeric>
4fd800b3a8 2011-02-23        kinaba: #include <iterator>
4fd800b3a8 2011-02-23        kinaba: #include <functional>
4fd800b3a8 2011-02-23        kinaba: #include <complex>
4fd800b3a8 2011-02-23        kinaba: #include <queue>
4fd800b3a8 2011-02-23        kinaba: #include <stack>
4fd800b3a8 2011-02-23        kinaba: #include <cmath>
4fd800b3a8 2011-02-23        kinaba: #include <cassert>
4fd800b3a8 2011-02-23        kinaba: #include <cstring>
4fd800b3a8 2011-02-23        kinaba: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: typedef complex<double> CMP;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: static const int MODVAL = 1000000009;
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: class Passwords { public:
4fd800b3a8 2011-02-23        kinaba: 	int countValid(int N, int L, int U, int D)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		FAC_INIT(200000);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		//  Sigma_{D<=d<=N-U-L} [C(N,d) 10^d Sigma_{L<=l,U<=u,u+l=N-d}[ C(N-d,u) 26^u 26^l ] ]
4fd800b3a8 2011-02-23        kinaba: 		//= Sigma_{D<=d<=N-U-L} [C(N,d) 10^d 26^(N-d) Sigma_{U<=u<=N-d-L}[ C(N-d,u) ] ]
4fd800b3a8 2011-02-23        kinaba: 		//   let f(N') = Sigma_{U<=u<=N'-L}[ C(N',u) ]
4fd800b3a8 2011-02-23        kinaba: 		//      then by Pascal's triangle, f(N') = 2*f(N'-1)+C(N'-1,U-1)+C(N'-1,N'-L)
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		mint answer=0, f=C(U+L,U);
4fd800b3a8 2011-02-23        kinaba: 		for(int d=N-U-L; d>=D; --d)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			answer = answer + C(N,d)*POW(10,d)*POW(26,N-d)*f;
4fd800b3a8 2011-02-23        kinaba: 			f = f*2 + C(N-d,U-1) + C(N-d, N-d-L+1);
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return answer.val;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: #include <ctime>
4fd800b3a8 2011-02-23        kinaba: double start_time; string timer()
4fd800b3a8 2011-02-23        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
4fd800b3a8 2011-02-23        kinaba:  { os << "{ ";
4fd800b3a8 2011-02-23        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
4fd800b3a8 2011-02-23        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
4fd800b3a8 2011-02-23        kinaba: void verify_case(const int& Expected, const int& Received) {
4fd800b3a8 2011-02-23        kinaba:  bool ok = (Expected == Received);
4fd800b3a8 2011-02-23        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
4fd800b3a8 2011-02-23        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
4fd800b3a8 2011-02-23        kinaba: #define END	 verify_case(_, Passwords().countValid(N, L, U, D));}
4fd800b3a8 2011-02-23        kinaba: int main(){
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: CASE(0)
4fd800b3a8 2011-02-23        kinaba: 	int N = 2;
4fd800b3a8 2011-02-23        kinaba: 	int L = 0;
4fd800b3a8 2011-02-23        kinaba: 	int U = 0;
4fd800b3a8 2011-02-23        kinaba: 	int D = 2;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 100;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int N = 3;
4fd800b3a8 2011-02-23        kinaba: 	int L = 1;
4fd800b3a8 2011-02-23        kinaba: 	int U = 1;
4fd800b3a8 2011-02-23        kinaba: 	int D = 1;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 40560;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int N = 4;
4fd800b3a8 2011-02-23        kinaba: 	int L = 1;
4fd800b3a8 2011-02-23        kinaba: 	int U = 1;
4fd800b3a8 2011-02-23        kinaba: 	int D = 1;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 5029440;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int N = 10;
4fd800b3a8 2011-02-23        kinaba: 	int L = 1;
4fd800b3a8 2011-02-23        kinaba: 	int U = 3;
4fd800b3a8 2011-02-23        kinaba: 	int D = 3;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 818019214;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int N = 5;
4fd800b3a8 2011-02-23        kinaba: 	int L = 2;
4fd800b3a8 2011-02-23        kinaba: 	int U = 2;
4fd800b3a8 2011-02-23        kinaba: 	int D = 2;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int N = 199201;
4fd800b3a8 2011-02-23        kinaba: 	int L = 0;
4fd800b3a8 2011-02-23        kinaba: 	int U = 70000;
4fd800b3a8 2011-02-23        kinaba: 	int D = 0;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 943311211;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(6)
4fd800b3a8 2011-02-23        kinaba: 	int N = 200000;
4fd800b3a8 2011-02-23        kinaba: 	int L = 11;
4fd800b3a8 2011-02-23        kinaba: 	int U = 111;
4fd800b3a8 2011-02-23        kinaba: 	int D = 1111;
4fd800b3a8 2011-02-23        kinaba: 	int _ = 298235838;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE