<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 {
private:
    bool rec(vector<int>& nums, int mask, int s, int su, string str, map<int,bool>& dp){
        if(dp.find(mask)!=dp.end()) return dp[mask];
        int aa = (1<<nums.size())-1;
        if(aa == mask) return true;
        int a = 1;
        if(s == 0) s = su;
        for(int i=0;i<nums.size();i++,a=a*2){
            if((a&mask) !=0 || nums[i]>s){
                continue;
            }
            if(rec(nums, (mask|a), s-nums[i], su, str+"  ", dp)){
                return true;
            }
        }
        dp[mask] = false;
        return false;
    }
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        for(auto num:nums){
            sum+=num;
        }
        map<int,bool> dp;
        return (sum%k==0) && rec(nums, 0, sum/k, sum/k, "", dp);
    }
};
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