Artifact 244c2d068d085457b322ecc642e87b6596f6b786
#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const int MODVAL = 1000000009;
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)); }
class Passwords { public:
int countValid(int N, int L, int U, int D)
{
FAC_INIT(200000);
// 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 ] ]
//= Sigma_{D<=d<=N-U-L} [C(N,d) 10^d 26^(N-d) Sigma_{U<=u<=N-d-L}[ C(N-d,u) ] ]
// let f(N') = Sigma_{U<=u<=N'-L}[ C(N',u) ]
// then by Pascal's triangle, f(N') = 2*f(N'-1)+C(N'-1,U-1)+C(N'-1,N'-L)
mint answer=0, f=C(U+L,U);
for(int d=N-U-L; d>=D; --d)
{
answer = answer + C(N,d)*POW(10,d)*POW(26,N-d)*f;
f = f*2 + C(N-d,U-1) + C(N-d, N-d-L+1);
}
return answer.val;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, Passwords().countValid(N, L, U, D));}
int main(){
CASE(0)
int N = 2;
int L = 0;
int U = 0;
int D = 2;
int _ = 100;
END
CASE(1)
int N = 3;
int L = 1;
int U = 1;
int D = 1;
int _ = 40560;
END
CASE(2)
int N = 4;
int L = 1;
int U = 1;
int D = 1;
int _ = 5029440;
END
CASE(3)
int N = 10;
int L = 1;
int U = 3;
int D = 3;
int _ = 818019214;
END
CASE(4)
int N = 5;
int L = 2;
int U = 2;
int D = 2;
int _ = 0;
END
CASE(5)
int N = 199201;
int L = 0;
int U = 70000;
int D = 0;
int _ = 943311211;
END
CASE(6)
int N = 200000;
int L = 11;
int U = 111;
int D = 1111;
int _ = 298235838;
END
}
// END CUT HERE