<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <code>true</code> if it is possible to divide this array into <code>k</code> non-empty subsets whose sums are all equal.</p>

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

<pre>
<strong>Input:</strong> nums = [4,3,2,3,5,2,1], k = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> It is possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], k = 3
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li>The frequency of each element is in the range <code>[1, 4]</code>.</li>
</ul>

class Solution {
    map<pair<int, int>, bool> dp;
public:
    bool helper(vector<int>& nums, int t_sum, int k, int r_sum, int bitmask) {
        // cout<<k<<" "<<r_sum<< " "<<bitmask<<" "<<((1<<nums.size())-1)<<endl;
        if (k == 0 && (bitmask == (1<<nums.size())-1)) return true;
        if ((bitmask == (1<<nums.size())-1) || k == 0) return false;

        // cout << "+" << endl;
        if (dp.find(make_pair(bitmask, k)) != dp.end()) return dp[make_pair(bitmask, k)];

        for (int i = 0; i < nums.size(); ++i)
        {
            // cout << i << endl;
            // cout << (bitmask & (1<<i)) << " " << (r_sum + nums[i]) << endl;
            if (((bitmask & (1<<i)) == 0) && (r_sum + nums[i] <= t_sum)) {

                if (r_sum + nums[i] == t_sum)
                    if (helper(nums, t_sum, k-1, 0, bitmask | (1<<i)))
                        return dp[make_pair(bitmask, k)]= true;
                // else 
                    // cout << "here" << endl;
                if (helper(nums, t_sum, k, r_sum + nums[i], bitmask | (1<<i)))
                    return dp[make_pair(bitmask, k)]= true;
            }
        }

        // cout << "-" << endl;
        return dp[make_pair(bitmask, k)]= false;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        long long int sum = 0;
        for (auto& n:nums) sum+=n;
        if (sum %k) return false;
        sum /= k;
        cout<<sum<<endl;
        return helper(nums, sum, k, 0, 0);
    }
};

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