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 <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: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: static const LL MODVAL = 1234567891;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: LL ADD(LL x, LL y) { return (x+y)%MODVAL; }
4fd800b3a8 2011-02-23        kinaba: LL SUB(LL x, LL y) { return (x-y+MODVAL)%MODVAL; }
4fd800b3a8 2011-02-23        kinaba: LL MUL(LL x, LL y) { return (x*y)%MODVAL; }
4fd800b3a8 2011-02-23        kinaba: LL POW(LL x, LL e) {
4fd800b3a8 2011-02-23        kinaba: 	LL v = 1;
4fd800b3a8 2011-02-23        kinaba: 	for(;e;x=MUL(x,x),e>>=1)
4fd800b3a8 2011-02-23        kinaba: 		if(e&1)
4fd800b3a8 2011-02-23        kinaba: 			v = MUL(v, x);
4fd800b3a8 2011-02-23        kinaba: 	return v;
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: LL DIV(LL x, LL y) { return MUL(x, POW(y, MODVAL-2)); }
4fd800b3a8 2011-02-23        kinaba: LL C(LL n, LL k) {
4fd800b3a8 2011-02-23        kinaba: 	LL v = 1;
4fd800b3a8 2011-02-23        kinaba: 	for(LL i=1; i<=k; ++i)
4fd800b3a8 2011-02-23        kinaba: 		v = DIV(MUL(v, n-i+1), i);
4fd800b3a8 2011-02-23        kinaba: 	return v;
4fd800b3a8 2011-02-23        kinaba: }
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: class TheLongPalindrome
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	int count(int n, int k)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		LL ans = 0;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=1; i<=k; ++i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			LL aa = f(i,i,n);
4fd800b3a8 2011-02-23        kinaba: 			for(int j=i-1; j>=1; --j)
4fd800b3a8 2011-02-23        kinaba: 				aa = (i-j)%2
4fd800b3a8 2011-02-23        kinaba: 				  ? SUB(aa, MUL(f(j,i,n), C(i,j)))
4fd800b3a8 2011-02-23        kinaba: 				  : ADD(aa, MUL(f(j,i,n), C(i,j)));
4fd800b3a8 2011-02-23        kinaba: 			ans = ADD(ans, MUL(aa, C(26,i)));
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return ans;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	LL f(LL i, LL b, LL n) // i^b + i^b + i^b+1 + i^b+1 + ... + (nth)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		LL v = MUL(GSS(i, b, n/2), 2);
4fd800b3a8 2011-02-23        kinaba: 		if( n%2 == 1 )
4fd800b3a8 2011-02-23        kinaba: 			v = ADD(v, POW(i, n/2+1));
4fd800b3a8 2011-02-23        kinaba: 		return v;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: 	public:
4fd800b3a8 2011-02-23        kinaba: 	void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); }
4fd800b3a8 2011-02-23        kinaba: 	private:
4fd800b3a8 2011-02-23        kinaba: 	template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: 	void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_0() { int Arg0 = 1; int Arg1 = 1; int Arg2 = 26; verify_case(0, Arg2, count(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_1() { int Arg0 = 2; int Arg1 = 10; int Arg2 = 52; verify_case(1, Arg2, count(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_2() { int Arg0 = 3; int Arg1 = 2; int Arg2 = 728; verify_case(2, Arg2, count(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_3() { int Arg0 = 44; int Arg1 = 7; int Arg2 = 240249781; verify_case(3, Arg2, count(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: int main() { TheLongPalindrome().run_test(-1); }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE