<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 solve(int mask, int targetSum, vector<int>& nums,int currSum, vector<int>& dp){
        if(1<<nums.size() == mask + 1){
            return currSum == targetSum;
        }
        if(currSum>targetSum)   return false;
        if(currSum == targetSum){
            currSum = 0;
        }
        if(dp[mask] != -1){
            return dp[mask];
        }
        bool ans = false;
        for(int i=0;i<nums.size();i++){
            if(!((1<<i) & mask)){
                ans |= solve(mask | 1<<i, targetSum, nums, currSum + nums[i], dp);
            }
        }
        return dp[mask] = ans;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        vector<int> dp(1<<nums.size(), -1);
        for(int num: nums){
            sum += num;
        }
        if(sum%k != 0)  return false;
        int newTargetSum = sum/k;
        return solve(0, newTargetSum, nums, 0, dp);
    }
};
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