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
function canDistribute(nums: number[], quantity: number[]): boolean {
    const m = quantity.length;
    const s: number[] = new Array(1 << m).fill(0);
    for (let i = 1; i < 1 << m; ++i) {
        for (let j = 0; j < m; ++j) {
            if ((i >> j) & 1) {
                s[i] = s[i ^ (1 << j)] + quantity[j];
                break;
            }
        }
    }
    const cnt: Map<number, number> = new Map();
    for (const x of nums) {
        cnt.set(x, (cnt.get(x) || 0) + 1);
    }
    const n = cnt.size;
    const arr: number[] = [];
    for (const [_, v] of cnt) {
        arr.push(v);
    }
    const f: boolean[][] = new Array(n).fill(false).map(() => new Array(1 << m).fill(false));
    for (let i = 0; i < n; ++i) {
        f[i][0] = true;
    }
    for (let i = 0; i < n; ++i) {
        for (let j = 0; j < 1 << m; ++j) {
            if (i > 0 && f[i - 1][j]) {
                f[i][j] = true;
                continue;
            }
            for (let k = j; k > 0; k = (k - 1) & j) {
                const ok1: boolean = (i == 0 && j == k) || (i > 0 && f[i - 1][j ^ k]);
                const ok2: boolean = s[k] <= arr[i];
                if (ok1 && ok2) {
                    f[i][j] = true;
                    break;
                }
            }
        }
    }
    return f[n - 1][(1 << m) - 1];
}
