96fdfab500 2011-03-20        kinaba: #include <iostream>
96fdfab500 2011-03-20        kinaba: #include <sstream>
96fdfab500 2011-03-20        kinaba: #include <iomanip>
96fdfab500 2011-03-20        kinaba: #include <vector>
96fdfab500 2011-03-20        kinaba: #include <string>
96fdfab500 2011-03-20        kinaba: #include <map>
96fdfab500 2011-03-20        kinaba: #include <set>
96fdfab500 2011-03-20        kinaba: #include <algorithm>
96fdfab500 2011-03-20        kinaba: #include <numeric>
96fdfab500 2011-03-20        kinaba: #include <iterator>
96fdfab500 2011-03-20        kinaba: #include <functional>
96fdfab500 2011-03-20        kinaba: #include <complex>
96fdfab500 2011-03-20        kinaba: #include <queue>
96fdfab500 2011-03-20        kinaba: #include <stack>
96fdfab500 2011-03-20        kinaba: #include <cmath>
96fdfab500 2011-03-20        kinaba: #include <cassert>
96fdfab500 2011-03-20        kinaba: #include <cstring>
96fdfab500 2011-03-20        kinaba: using namespace std;
96fdfab500 2011-03-20        kinaba: typedef long long LL;
96fdfab500 2011-03-20        kinaba: typedef complex<double> CMP;
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: static const int MODVAL = 500500573;
96fdfab500 2011-03-20        kinaba: struct mint
96fdfab500 2011-03-20        kinaba: {
96fdfab500 2011-03-20        kinaba: 	int val;
96fdfab500 2011-03-20        kinaba: 	mint():val(0){}
96fdfab500 2011-03-20        kinaba: 	mint(int x):val(x%MODVAL) {}
96fdfab500 2011-03-20        kinaba: 	mint(LL  x):val(x%MODVAL) {}
96fdfab500 2011-03-20        kinaba: };
96fdfab500 2011-03-20        kinaba: mint operator+(mint x, mint y) { return x.val+y.val; }
96fdfab500 2011-03-20        kinaba: mint operator-(mint x, mint y) { return x.val-y.val+MODVAL; }
96fdfab500 2011-03-20        kinaba: mint operator*(mint x, mint y) { return LL(x.val)*y.val; }
96fdfab500 2011-03-20        kinaba: mint POW(mint x, int e) {
96fdfab500 2011-03-20        kinaba: 	mint v = 1;
96fdfab500 2011-03-20        kinaba: 	for(;e;x=x*x,e>>=1)
96fdfab500 2011-03-20        kinaba: 		if(e&1)
96fdfab500 2011-03-20        kinaba: 			v=v*x;
96fdfab500 2011-03-20        kinaba: 	return v;
96fdfab500 2011-03-20        kinaba: }
96fdfab500 2011-03-20        kinaba: mint operator/(mint x, mint y) { return x * POW(y, MODVAL-2); }
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: class ProductAndSum { public:
96fdfab500 2011-03-20        kinaba: 	int getSum(int p2, int p3, int p5, int p7, int S)
96fdfab500 2011-03-20        kinaba: 	{
96fdfab500 2011-03-20        kinaba: 		// Precomputing n!, 1/n!, and 111...111
96fdfab500 2011-03-20        kinaba: 		vector<mint> FACT(2501), FACT_INV(2501), ONES(2501);
96fdfab500 2011-03-20        kinaba: 		FACT[0] = FACT_INV[0] = 1;
96fdfab500 2011-03-20        kinaba: 		ONES[0] = 0;
96fdfab500 2011-03-20        kinaba: 		for(int n=1; n<FACT.size(); ++n)
96fdfab500 2011-03-20        kinaba: 		{
96fdfab500 2011-03-20        kinaba: 			FACT[n] = FACT[n-1] * n;
96fdfab500 2011-03-20        kinaba: 			FACT_INV[n] = 1 / FACT[n];
96fdfab500 2011-03-20        kinaba: 			ONES[n] = ONES[n-1]*10 + 1;
96fdfab500 2011-03-20        kinaba: 		}
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: 		mint answer = 0;
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: 		// Exhaustive search over the number of 4,6,8,9s : at most 33*50*50*100 < 8M iterations
96fdfab500 2011-03-20        kinaba: 		for(int v8=0; v8*3<=p2; ++v8)
96fdfab500 2011-03-20        kinaba: 		for(int v4=0; v4*2+v8*3<=p2; ++v4)
96fdfab500 2011-03-20        kinaba: 		for(int v9=0; v9*2<=p3; ++v9)
96fdfab500 2011-03-20        kinaba: 		for(int v6=0; v6+v4*2+v8*3<=p2 && v6+v9*2<=p3; ++v6)
96fdfab500 2011-03-20        kinaba: 		{
96fdfab500 2011-03-20        kinaba: 			// then, the number of 1,2,3s are computable
96fdfab500 2011-03-20        kinaba: 			int v[] = {-1, -1, p2-v8*3-v4*2-v6, p3-v9*2-v6, v4, p5, v6, p7, v8, v9};
96fdfab500 2011-03-20        kinaba: 			{
96fdfab500 2011-03-20        kinaba: 				int v1 = S;
96fdfab500 2011-03-20        kinaba: 				for(int i=2; i<=9; ++i)
96fdfab500 2011-03-20        kinaba: 					v1 -= i * v[i];
96fdfab500 2011-03-20        kinaba: 				if( v1 < 0 )
96fdfab500 2011-03-20        kinaba: 					continue;
96fdfab500 2011-03-20        kinaba: 				v[1] = v1;
96fdfab500 2011-03-20        kinaba: 			}
96fdfab500 2011-03-20        kinaba: 			int N = accumulate(v+1, v+10, 0);
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: 			// Now, let's compute the sum of all integers, who have N digits and #d = v[d], in constant time!
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: 			// It can be calculated as follows:
96fdfab500 2011-03-20        kinaba: 			//   Q: how many of the integers have, say "1" in the last digit?
96fdfab500 2011-03-20        kinaba: 			//   A: it is, of course, C(N-1, v[1]-1, v[2], ..., v[9])
96fdfab500 2011-03-20        kinaba: 			//      where C(k,a,b,..) is the # of ways of spliting k elements into groups of size a, b, ...
96fdfab500 2011-03-20        kinaba: 			// So, the sum of the least digits of the integers are
96fdfab500 2011-03-20        kinaba: 			//   X = \Sigma_{d=1..9} (d * C(N-1, v[1], v[2], ..., v[d]-1, ..., v[9]))
96fdfab500 2011-03-20        kinaba: 			// By the same argument, the sum of the second-last digits (10-no-kurai in japanese) is
96fdfab500 2011-03-20        kinaba: 			//   10 * X
96fdfab500 2011-03-20        kinaba: 			// For hundreds, the sum is 100*X, and so on. Eventualy, the sum of whole integers is
96fdfab500 2011-03-20        kinaba: 			//   t = (1+10+...+10^N) * X
96fdfab500 2011-03-20        kinaba: 			//     = 111...111 * \Sigma_{d=1..9} (d * C(N-1, v[1], v[2], ..., v[d]-1, ..., v[9]))
96fdfab500 2011-03-20        kinaba: 			// Let us simplify the formula by using C(k,a,b,...) = k! / a!b!...
96fdfab500 2011-03-20        kinaba: 			//   t = 111...111 * \Sigma_{d=1..9} (d * (N-1)! / v[1]! / ... / v[9]! * v[d])
96fdfab500 2011-03-20        kinaba: 			//     = 111...111 * (N-1)! / v[1]! / ... / v[9]! * \Sigma_{d=1..9} (d*v[d])
96fdfab500 2011-03-20        kinaba: 			//     = 111...111 * (N-1)! / v[1]! / ... / v[9]! * S
96fdfab500 2011-03-20        kinaba: 			// That's it!
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: 			mint t = ONES[N] * FACT[N-1] * S;
96fdfab500 2011-03-20        kinaba: 			for(int i=1; i<=9; ++i)
96fdfab500 2011-03-20        kinaba: 				t = t * FACT_INV[v[i]];
96fdfab500 2011-03-20        kinaba: 			answer = answer + t;
96fdfab500 2011-03-20        kinaba: 		}
96fdfab500 2011-03-20        kinaba: 		return answer.val;
96fdfab500 2011-03-20        kinaba: 	}
96fdfab500 2011-03-20        kinaba: };
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: // BEGIN CUT HERE
96fdfab500 2011-03-20        kinaba: #include <ctime>
96fdfab500 2011-03-20        kinaba: double start_time; string timer()
96fdfab500 2011-03-20        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
96fdfab500 2011-03-20        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
96fdfab500 2011-03-20        kinaba:  { os << "{ ";
96fdfab500 2011-03-20        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
96fdfab500 2011-03-20        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
96fdfab500 2011-03-20        kinaba: void verify_case(const int& Expected, const int& Received) {
96fdfab500 2011-03-20        kinaba:  bool ok = (Expected == Received);
96fdfab500 2011-03-20        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
96fdfab500 2011-03-20        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
96fdfab500 2011-03-20        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
96fdfab500 2011-03-20        kinaba: #define END	 verify_case(_, ProductAndSum().getSum(p2, p3, p5, p7, S));}
96fdfab500 2011-03-20        kinaba: int main(){
96fdfab500 2011-03-20        kinaba: 
96fdfab500 2011-03-20        kinaba: CASE(0)
96fdfab500 2011-03-20        kinaba: 	int p2 = 2;
96fdfab500 2011-03-20        kinaba: 	int p3 = 0;
96fdfab500 2011-03-20        kinaba: 	int p5 = 0;
96fdfab500 2011-03-20        kinaba: 	int p7 = 0;
96fdfab500 2011-03-20        kinaba: 	int S = 4;
96fdfab500 2011-03-20        kinaba: 	int _ = 26;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: CASE(1)
96fdfab500 2011-03-20        kinaba: 	int p2 = 0;
96fdfab500 2011-03-20        kinaba: 	int p3 = 0;
96fdfab500 2011-03-20        kinaba: 	int p5 = 0;
96fdfab500 2011-03-20        kinaba: 	int p7 = 0;
96fdfab500 2011-03-20        kinaba: 	int S = 10;
96fdfab500 2011-03-20        kinaba: 	int _ = 110109965;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: CASE(2)
96fdfab500 2011-03-20        kinaba: 	int p2 = 2;
96fdfab500 2011-03-20        kinaba: 	int p3 = 0;
96fdfab500 2011-03-20        kinaba: 	int p5 = 0;
96fdfab500 2011-03-20        kinaba: 	int p7 = 0;
96fdfab500 2011-03-20        kinaba: 	int S = 5;
96fdfab500 2011-03-20        kinaba: 	int _ = 610;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: CASE(3)
96fdfab500 2011-03-20        kinaba: 	int p2 = 1;
96fdfab500 2011-03-20        kinaba: 	int p3 = 1;
96fdfab500 2011-03-20        kinaba: 	int p5 = 1;
96fdfab500 2011-03-20        kinaba: 	int p7 = 1;
96fdfab500 2011-03-20        kinaba: 	int S = 10;
96fdfab500 2011-03-20        kinaba: 	int _ = 0;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: CASE(4)
96fdfab500 2011-03-20        kinaba: 	int p2 = 5;
96fdfab500 2011-03-20        kinaba: 	int p3 = 5;
96fdfab500 2011-03-20        kinaba: 	int p5 = 5;
96fdfab500 2011-03-20        kinaba: 	int p7 = 5;
96fdfab500 2011-03-20        kinaba: 	int S = 100;
96fdfab500 2011-03-20        kinaba: 	int _ = 61610122;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: CASE(5)
96fdfab500 2011-03-20        kinaba: 	int p2 = 100;
96fdfab500 2011-03-20        kinaba: 	int p3 = 100;
96fdfab500 2011-03-20        kinaba: 	int p5 = 100;
96fdfab500 2011-03-20        kinaba: 	int p7 = 100;
96fdfab500 2011-03-20        kinaba: 	int S = 2500;
96fdfab500 2011-03-20        kinaba: 	int _ = -1;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: /*
96fdfab500 2011-03-20        kinaba: CASE(6)
96fdfab500 2011-03-20        kinaba: 	int p2 = ;
96fdfab500 2011-03-20        kinaba: 	int p3 = ;
96fdfab500 2011-03-20        kinaba: 	int p5 = ;
96fdfab500 2011-03-20        kinaba: 	int p7 = ;
96fdfab500 2011-03-20        kinaba: 	int S = ;
96fdfab500 2011-03-20        kinaba: 	int _ = ;
96fdfab500 2011-03-20        kinaba: END
96fdfab500 2011-03-20        kinaba: */
96fdfab500 2011-03-20        kinaba: }
96fdfab500 2011-03-20        kinaba: // END CUT HERE