<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 visitedAllMask = 0;
    // int dp[(1 << 16) + 1][17][40001];
    unordered_map<string, bool> dp;

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        for (int num : nums) {
            sum += num;
        }

        if (sum % k != 0) {
            return false;
        }

        // memset(dp, -1, sizeof(dp));
        int targetSum = sum / k;
        visitedAllMask = (1 << nums.size()) - 1;

        return solve(0, 0, 0, k, targetSum, nums);
    }

    bool solve(int mask, int ki, int curSum, const int k, const int targetSum, const vector<int>& nums) {
        if (ki == k && mask == visitedAllMask) {
            return true;
        }

        if (curSum > targetSum) {
            return false;
        }

        // if (dp[mask][ki][curSum] != -1) {
        //     return dp[mask][ki][curSum];
        // }
        string key = getKey(mask, ki, curSum);
        if (dp.contains(key)) {
            return dp[key];
        }

        bool res = false;
        for (int i = 0; i < nums.size(); i++) {
            bool visited = (mask >> i) & 1;

            if (!visited) {
                int newMask = mask | (1 << i);
                int newCurSum = curSum + nums[i];
                

                if (newCurSum == targetSum) {
                    res = solve(newMask, ki+1, 0, k, targetSum, nums);
                } else {
                    res = solve(newMask, ki, newCurSum, k, targetSum, nums);
                }

                if (res) {
                    break;
                }
            }
        }

        return dp[key] = res;
    }

    string getKey(int mask, int ki, int curSum) {
        return to_string(mask) + "_" + to_string(ki) + "_" + to_string(curSum);
    }
};
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