<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:
    int box[17];
    int sum , K , share;
    bool f(int i , vector<int> &nums){
        if(i == nums.size()){
            for(int i=0;i<K;i++){
                if(box[i] != box[0] || box[i] == 0) return false;
            }
            return true;
        }else{
            unordered_map<int,int> called;
            for(int j=0;j<K;j++){
                if(called[box[j]]) continue;
                else                called[box[j]]++;
                if((box[j] + nums[i]) > (share))  continue;
                box[j] += nums[i];
                if(box[j] > (share)){
                    box[j] -= nums[i];
                    continue;
                }
                if(f(i+1 , nums))   return true;
                box[j] -= nums[i];
            }
            return false;
        }
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        memset(&box[0] , 0 , sizeof(box));
        K = k;
        sum = accumulate(nums.begin() , nums.end() , 0);
        if(sum % k) return false;
        share = sum / K;
        for(int i=0;i<nums.size();i++)    if(nums[i] > (share))   return false;
        // for(int i=0;i<nums.size();i++){
        //     for(int j=0;j<nums.size()-1;j++){
        //         if(nums[j] < nums[j+1]) swap(nums[j] , nums[j+1]);
        //     }
        // }
        sort(nums.rbegin() , nums.rend());
        return f(0 , nums);
    }
};
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