Averaging the Average

#include <bits/stdc++.h>

using namespace std;

const int N = 34;

int A[N], dp[2][N][N][101][101];

int main () {
    int n, k, total = 0;
    cin >> n >> k;

    for (int i = 0; i < n; i++) {
        cin >> A[i];
        total += A[i];
    }

    dp[0][0][0][0][0] = true;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j <= i; j++) {
            for (int z = 0; z <= i; z++) {
                for (int l = 0; l <= 100; l++) {
                    for (int m = 0; m <= 100; m++) {
                        dp[(i + 1) & 1][j + 1][z][l + A[i]][m] |= dp[i & 1][j][z][l][m];
                        dp[(i + 1) & 1][j][z + 1][l][m + A[i]] |= dp[i & 1][j][z][l][m];
                        dp[(i + 1) & 1][j][z][l][m] |= dp[i & 1][j][z][l][m];
                    }
                }
            }
        }
    }

    int num = 0, den = 1;
    int diffNum = k, diffDen = 1;
    for (int i = 1; i < n; i++) {
        for (int j = 1; j < n; j++) {
            int z = n - i - j;

            if (z <= 0)
                continue;

            for (int c1 = 1; c1 < 100; c1++) {
                for (int c2 = 1; c2 < 100; c2++) {
                    int c3 = total - c1 - c2;

                    if (!dp[n & 1][i][j][c1][c2])
                        continue;

                    int tmpNum = j * z * c1 + i * z * c2 + i * j * c3;
                    int tmpDen = 3 * i * j * z;
                    int tmp = abs (tmpNum - k * i * j * z * 3);

                    if (tmp * diffDen < tmpDen * diffNum) {
                        diffNum = tmp, diffDen = tmpDen;
                        num = tmpNum, den = tmpDen;
                    } else if (tmp * diffDen == tmpDen * diffNum && tmpNum < 3 * k * i * j * z) {
                        diffNum = tmp, diffDen = tmpDen;
                        num = tmpNum, den = tmpDen;
                    }
                }
            }
        }
    }

    int g = __gcd (num, den);
    cout << num / g << '/' << den / g << "\n";

    return 0;
}