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Artifact e110c16d9a9bffd53f881091cd58d56f4e3f1779


#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
using namespace std;
typedef long long LL;

static const LL MODVAL = 1234567891;

LL ADD(LL x, LL y) { return (x+y)%MODVAL; }
LL SUB(LL x, LL y) { return (x-y+MODVAL)%MODVAL; }
LL MUL(LL x, LL y) { return (x*y)%MODVAL; }
LL POW(LL x, LL e) {
	LL v = 1;
	for(;e;x=MUL(x,x),e>>=1)
		if(e&1)
			v = MUL(v, x);
	return v;
}
LL DIV(LL x, LL y) { return MUL(x, POW(y, MODVAL-2)); }
LL C(LL n, LL k) {
	LL v = 1;
	for(LL i=1; i<=k; ++i)
		v = DIV(MUL(v, n-i+1), i);
	return v;
}
LL GSS(LL k, LL b, LL e) // k^b + k^b+1 + ... + k^e
{
	if( b >  e ) return 0;
	if( k <= 1 ) return k*(e-b+1);
	return DIV(SUB(POW(k, e+1), POW(k,b)), k-1);
}

class TheLongPalindrome
{
public:
	int count(int n, int k) 
	{
		LL ans = 0;
		for(int i=1; i<=k; ++i)
		{
			LL aa = f(i,i,n);
			for(int j=i-1; j>=1; --j)
				aa = (i-j)%2
				  ? SUB(aa, MUL(f(j,i,n), C(i,j)))
				  : ADD(aa, MUL(f(j,i,n), C(i,j)));
			ans = ADD(ans, MUL(aa, C(26,i)));
		}
		return ans;
	}

	LL f(LL i, LL b, LL n) // i^b + i^b + i^b+1 + i^b+1 + ... + (nth)
	{
		LL v = MUL(GSS(i, b, n/2), 2);
		if( n%2 == 1 )
			v = ADD(v, POW(i, n/2+1));
		return v;
	}

// BEGIN CUT HERE
	public:
	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(); }
	private:
	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(); }
	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; } }
	void test_case_0() { int Arg0 = 1; int Arg1 = 1; int Arg2 = 26; verify_case(0, Arg2, count(Arg0, Arg1)); }
	void test_case_1() { int Arg0 = 2; int Arg1 = 10; int Arg2 = 52; verify_case(1, Arg2, count(Arg0, Arg1)); }
	void test_case_2() { int Arg0 = 3; int Arg1 = 2; int Arg2 = 728; verify_case(2, Arg2, count(Arg0, Arg1)); }
	void test_case_3() { int Arg0 = 44; int Arg1 = 7; int Arg2 = 240249781; verify_case(3, Arg2, count(Arg0, Arg1)); }

// END CUT HERE
};
// BEGIN CUT HERE 
int main() { TheLongPalindrome().run_test(-1); }
// END CUT HERE