<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>

from typing import List
import heapq

class Solution:
    def getFinalState(self, nums: List[int], k: int, multiplier: int) -> List[int]:
        MOD = 10**9 + 7
        
        # If multiplier is 1, no changes are needed, return the original list.
        if multiplier == 1:
            return nums
        
        # Create a priority queue (min-heap) with (value, index) tuples.
        pq = [(num, i) for i, num in enumerate(nums)]
        heapq.heapify(pq)
        
        # Get the maximum value from the original nums list.
        max_val = max(nums)
        
        # Perform k operations of replacing the minimum value with its multiplied version.
        while k > 0 and pq[0][0] < max_val:
            min_val, idx = heapq.heappop(pq)
            heapq.heappush(pq, (min_val * multiplier, idx))
            k -= 1
        
        # Number of elements in nums
        n = len(nums)
        
        # Process the heap and update the nums list accordingly.
        pq.sort()
        for i, (val, idx) in enumerate(pq):
            # Compute the power of multiplier needed.
            multiplier_power = pow(multiplier, k // n + int(i < k % n), MOD)
            nums[idx] = (val * multiplier_power) % MOD
        
        return nums

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