<p>You are given an integer array <code>nums</code>.</p>

<p>You should move each element of <code>nums</code> into one of the two arrays <code>A</code> and <code>B</code> such that <code>A</code> and <code>B</code> are non-empty, and <code>average(A) == average(B)</code>.</p>

<p>Return <code>true</code> if it is possible to achieve that and <code>false</code> otherwise.</p>

<p><strong>Note</strong> that for an array <code>arr</code>, <code>average(arr)</code> is the sum of all the elements of <code>arr</code> over the length of <code>arr</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,1]
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 30</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    bool check(int idx, int n, int target, vector<int>& nums, vector<vector<vector<bool>>>& dp) {
        if (n == 0) {
            return target == 0;
        }
        if (idx == nums.size()) return false;
        if (dp[idx][n][target] == false) return false;
        bool take = false;
        if (target - nums[idx] >= 0) take = check(idx + 1, n - 1, target - nums[idx], nums, dp);
        if (take) return true;
        bool nTake = check(idx + 1, n, target, nums, dp);
        if (nTake) return true;
        return dp[idx][n][target] = false;
    }

    bool splitArraySameAverage(vector<int>& nums) {
        int N = nums.size();
        if (N < 2) return false;
        int S = 0;
        for (int e : nums) S += e;
        if (S == 0) return true;
        vector<vector<vector<bool>>> dp(N, vector<vector<bool>>(N, vector<bool>(S, true)));
        for (int n = 1; n < N; n++) {
            if ((S * n) % N == 0) {
                int s = (S * n) / N;
                if (check(0, n, s, nums, dp)) return true;
            }
        }
        return false;
    }
};

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