<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 {
public:
   bool f(int mask,int curr,int target,int k,vector<int>&nums,vector<int>&dp){
    if(k==1)return true;
    if(curr>target || __builtin_popcount(mask)==nums.size()){
        return false;
    }
    if(dp[mask]!=-1)return dp[mask];
    if(curr==target){
        k--;
        curr=0;
    }

    bool ans = false;
    for(int i=0; i<nums.size(); i++){
        if(!(mask&(1<<i))){
            ans|=f(mask|(1<<i),curr+nums[i],target,k,nums,dp);
        }
    }
    return dp[mask]=ans;
   }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        int n = nums.size();
        for(int i=0; i<n; i++){
            sum+=nums[i];
        }
        if(sum%k!=0)return false;
        vector<int>dp(1<<17,-1);
        return f(0,0,sum/k,k,nums,dp);
    }
};
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