<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:    
    unordered_map<int,int> dp;     
    bool dfs(vector<int> &nums,int &tot,int k,int ind,int mask,int sum)
    {
        if(k==1)
            return true;
        if(sum==0)
            return dfs(nums,tot,k-1,0,mask,tot);
        if(dp.find(mask)!=dp.end())
            return dp[mask];
        if(ind==nums.size())
            return false;
        bool pick=false,npick=false;
        int prev=mask;
        if(!(mask&(1<<ind)))
        {
            mask|=(1<<ind);
            if((sum-nums[ind])>=0)
                pick=dfs(nums,tot,k,ind+1,mask,sum-nums[ind]);
            if(pick)    
                return dp[mask] =  true;
            mask=prev;
        }
        npick=dfs(nums,tot,k,ind+1,mask,sum);
        return dp[mask] = npick;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) 
    {
        int n=nums.size(),tot=0;
        for(int &i:nums)
            tot+=i;
        if(tot%k)
            return false;
        tot/=k;
        return dfs(nums,tot,k,0,0,tot);
    }
};
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