<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>



class Solution:
    # def canDistribute(self, nums: List[int], quantity: List[int]) -> bool:
    #     cnt = Counter(Counter(nums).values())
    #     n = len(quantity)
    #
    #     # print(cnt)
    #     quantity.sort(key=lambda x: -x)
    #
    #     def dfs(i: int) -> bool:
    #         if i < 0: return True
    #         q = quantity[i]
    #         # if cnt[q] > 0:
    #         #     cnt[q] -= 1
    #         #     return dfs(i-1)
    #
    #         keys = sorted(cnt.keys(), key=lambda x:-x)
    #         for k in keys:
    #             if k >= q and cnt[k] > 0:
    #                 cnt[k] -= 1
    #                 cnt[k - q] += 1
    #                 if dfs(i - 1):
    #                     return True
    #                 cnt[k] += 1
    #                 cnt[k - q] -= 1
    #         return False
    #
    #     return dfs(n - 1)
    def canDistribute(self, nums: List[int], quantity: List[int]) -> bool:
        t = sorted(Counter(nums).values(), reverse = True)
        quantity.sort(reverse = True)
        def backtracking(idx):
            if idx == len(quantity): return True
            for i in range(len(t)):
                if t[i] >= quantity[idx]:
                    t[i] -= quantity[idx]
                    if backtracking(idx+1): return True
                    t[i] += quantity[idx]
            return False
        return backtracking(0)


if __name__ == '__main__':
    s = Solution()
    print(s.canDistribute([1, 1, 1, 1, 1], [2, 3]))


27900