#include <utility>
#include <vector>

std::vector< std::pair<int, int> > factor_table;
void fill_sieve( int n )
{
	factor_table.resize(n+1);
	for( int i = 1; i <= n; ++i )
		factor_table[i] = std::pair<int, int>(i, 1);
	for( int j = 2, j2 = 4; j2 <= n; (j2 += j), (j2 += ++j) ) {
		if (factor_table[j].second == 1) {
			int i = j;
			int ij = j2;
			while (ij <= n) {
				factor_table[ij] = std::pair<int, int>(j, i);
				++i;
				ij += j;
			}
		}
	}
}

std::vector<unsigned> powers;

template<int dir>
void factor( int num )
{
	while (num != 1) {
		powers[factor_table[num].first] += dir;
		num = factor_table[num].second;
	}
}

void calc_catalan(unsigned N)
{
    powers.resize(N+1);
    for( unsigned k = 2; k <= N; ++k ) {
         factor<+1>(k+N);
         factor<-1>(k);
    }
}

#include <iostream>
#include <cmath>
int main(void)
{
    fill_sieve(20000);
    unsigned N = 9913;
    calc_catalan(N);
    char* sep = "";
    for( unsigned i = 0; i < powers.size(); ++i ) {
    	if (powers[i]) {
    	    std::cout << sep << i;
    	    sep = " * ";
    	    if (powers[i] > 1)
    	        std::cout << "**" << powers[i];
    	}
    }
    std::cout << "\n\n";
}