<p>You are given an integer array <code>nums</code>, an integer <code>k</code>, and an integer <code>multiplier</code>.</p>

<p>You need to perform <code>k</code> operations on <code>nums</code>. In each operation:</p>

<ul>
	<li>Find the <strong>minimum</strong> value <code>x</code> in <code>nums</code>. If there are multiple occurrences of the minimum value, select the one that appears <strong>first</strong>.</li>
	<li>Replace the selected minimum value <code>x</code> with <code>x * multiplier</code>.</li>
</ul>

<p>After the <code>k</code> operations, apply <strong>modulo</strong> <code>10<sup>9</sup> + 7</code> to every value in <code>nums</code>.</p>

<p>Return an integer array denoting the <em>final state</em> of <code>nums</code> after performing all <code>k</code> operations and then applying the modulo.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [2,1,3,5,6], k = 5, multiplier = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">[8,4,6,5,6]</span></p>

<p><strong>Explanation:</strong></p>

<table>
	<tbody>
		<tr>
			<th>Operation</th>
			<th>Result</th>
		</tr>
		<tr>
			<td>After operation 1</td>
			<td>[2, 2, 3, 5, 6]</td>
		</tr>
		<tr>
			<td>After operation 2</td>
			<td>[4, 2, 3, 5, 6]</td>
		</tr>
		<tr>
			<td>After operation 3</td>
			<td>[4, 4, 3, 5, 6]</td>
		</tr>
		<tr>
			<td>After operation 4</td>
			<td>[4, 4, 6, 5, 6]</td>
		</tr>
		<tr>
			<td>After operation 5</td>
			<td>[8, 4, 6, 5, 6]</td>
		</tr>
		<tr>
			<td>After applying modulo</td>
			<td>[8, 4, 6, 5, 6]</td>
		</tr>
	</tbody>
</table>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [100000,2000], k = 2, multiplier = 1000000</span></p>

<p><strong>Output:</strong> <span class="example-io">[999999307,999999993]</span></p>

<p><strong>Explanation:</strong></p>

<table>
	<tbody>
		<tr>
			<th>Operation</th>
			<th>Result</th>
		</tr>
		<tr>
			<td>After operation 1</td>
			<td>[100000, 2000000000]</td>
		</tr>
		<tr>
			<td>After operation 2</td>
			<td>[100000000000, 2000000000]</td>
		</tr>
		<tr>
			<td>After applying modulo</td>
			<td>[999999307, 999999993]</td>
		</tr>
	</tbody>
</table>
</div>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= multiplier &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution:
    def getFinalState(self, nums: List[int], k: int, multiplier: int) -> List[int]:
        if multiplier==1:return nums
        def down(heap,i):
            while i*2+1<len(heap):
                small=i*2+1
                if i*2+2<len(heap) and nums[heap[i*2+2]]<nums[heap[small]]:
                    small=i*2+2
                elif i*2+2<len(heap) and nums[heap[i*2+2]]==nums[heap[small]] and heap[i*2+2]<heap[small]:
                    small=i*2+2
                if nums[heap[small]]<nums[heap[i]]:
                    heap[small],heap[i]=heap[i],heap[small]
                    i=small
                elif nums[heap[small]]==nums[heap[i]] and heap[i]>heap[small]:
                    heap[small],heap[i]=heap[i],heap[small]
                    i=small
                else:break
            return heap
        heap=[i for i in range(len(nums))]
        for i in range(len(nums)//2,-1,-1):
            heap=down(heap,i)
        visited=[0]*len(nums)
        co=0
        while co<len(nums) and k:
            nums[heap[0]]*=multiplier
            if visited[heap[0]]==0:co+=1
            visited[heap[0]]+=1
            heap=down(heap,0)
            k-=1
        if k==0:
            for i in range(len(nums)):nums[i]%=(10**9 +7)
        else:
            left=k%len(nums)
            for i in range(left):
                nums[heap[0]]*=multiplier
                heap=down(heap,0)
            for i in range(len(nums)):
                nums[i]*=pow(multiplier,k//len(nums),10**9 +7)
                nums[i]%=(10**9 +7)
        return nums
18700