Distribute Repeating Integers
<p>You are given an array of <code>n</code> integers, <code>nums</code>, where there are at most <code>50</code> unique values in the array. You are also given an array of <code>m</code> customer order quantities, <code>quantity</code>, where <code>quantity[i]</code> is the amount of integers the <code>i<sup>th</sup></code> customer ordered. Determine if it is possible to distribute <code>nums</code> such that:</p>

<ul>
	<li>The <code>i<sup>th</sup></code> customer gets <strong>exactly</strong> <code>quantity[i]</code> integers,</li>
	<li>The integers the <code>i<sup>th</sup></code> customer gets are <strong>all equal</strong>, and</li>
	<li>Every customer is satisfied.</li>
</ul>

<p>Return <code>true</code><em> if it is possible to distribute </em><code>nums</code><em> according to the above conditions</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4], quantity = [2]
<strong>Output:</strong> false
<strong>Explanation:</strong> The 0<sup>th</sup> customer cannot be given two different integers.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,3], quantity = [2]
<strong>Output:</strong> true
<strong>Explanation:</strong> The 0<sup>th</sup> customer is given [3,3]. The integers [1,2] are not used.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,2,2], quantity = [2,2]
<strong>Output:</strong> true
<strong>Explanation:</strong> The 0<sup>th</sup> customer is given [1,1], and the 1st customer is given [2,2].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>m == quantity.length</code></li>
	<li><code>1 &lt;= m &lt;= 10</code></li>
	<li><code>1 &lt;= quantity[i] &lt;= 10<sup>5</sup></code></li>
	<li>There are at most <code>50</code> unique values in <code>nums</code>.</li>
</ul>
Bit Manipulation; Array; Dynamic Programming; Backtracking; Bitmask
func canDistribute(nums []int, quantity []int) bool {
	m := len(quantity)
	s := make([]int, 1<<m)
	for i := 1; i < 1<<m; i++ {
		for j := 0; j < m; j++ {
			if i>>j&1 == 1 {
				s[i] = s[i^(1<<j)] + quantity[j]
				break
			}
		}
	}
	cnt := map[int]int{}
	for _, x := range nums {
		cnt[x]++
	}
	n := len(cnt)
	arr := make([]int, 0, n)
	for _, x := range cnt {
		arr = append(arr, x)
	}
	f := make([][]bool, n)
	for i := range f {
		f[i] = make([]bool, 1<<m)
		f[i][0] = true
	}
	for i := 0; i < n; i++ {
		for j := 0; j < 1<<m; j++ {
			if i > 0 && f[i-1][j] {
				f[i][j] = true
				continue
			}
			for k := j; k > 0; k = (k - 1) & j {
				ok1 := (i == 0 && j == k) || (i > 0 && f[i-1][j-k])
				ok2 := s[k] <= arr[i]
				if ok1 && ok2 {
					f[i][j] = true
					break
				}
			}
		}
	}
	return f[n-1][(1<<m)-1]
}