Prime Subtraction Operation
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>

<p>You can perform the following operation as many times as you want:</p>

<ul>
	<li>Pick an index <code>i</code> that you haven&rsquo;t picked before, and pick a prime <code>p</code> <strong>strictly less than</strong> <code>nums[i]</code>, then subtract <code>p</code> from <code>nums[i]</code>.</li>
</ul>

<p>Return <em>true if you can make <code>nums</code> a strictly increasing array using the above operation and false otherwise.</em></p>

<p>A <strong>strictly increasing array</strong> is an array whose each element is strictly greater than its preceding element.</p>

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

<pre>
<strong>Input:</strong> nums = [4,9,6,10]
<strong>Output:</strong> true
<strong>Explanation:</strong> In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums[0], so that nums becomes [1,9,6,10].
In the second operation: i = 1, p = 7, subtract 7 from nums[1], so nums becomes equal to [1,2,6,10].
After the second operation, nums is sorted in strictly increasing order, so the answer is true.</pre>

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

<pre>
<strong>Input:</strong> nums = [6,8,11,12]
<strong>Output:</strong> true
<strong>Explanation: </strong>Initially nums is sorted in strictly increasing order, so we don&#39;t need to make any operations.</pre>

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

<pre>
<strong>Input:</strong> nums = [5,8,3]
<strong>Output:</strong> false
<strong>Explanation:</strong> It can be proven that there is no way to perform operations to make nums sorted in strictly increasing order, so the answer is false.</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code><font face="monospace">nums.length == n</font></code></li>
</ul>
Greedy; Array; Math; Binary Search; Number Theory
function primeSubOperation(nums: number[]): boolean {
    const p: number[] = [];
    for (let i = 2; i <= 1000; ++i) {
        let ok = true;
        for (const j of p) {
            if (i % j === 0) {
                ok = false;
                break;
            }
        }
        if (ok) {
            p.push(i);
        }
    }
    const search = (x: number): number => {
        let l = 0;
        let r = p.length;
        while (l < r) {
            const mid = (l + r) >> 1;
            if (p[mid] > x) {
                r = mid;
            } else {
                l = mid + 1;
            }
        }
        return l;
    };
    const n = nums.length;
    for (let i = n - 2; i >= 0; --i) {
        if (nums[i] < nums[i + 1]) {
            continue;
        }
        const j = search(nums[i] - nums[i + 1]);
        if (j === p.length || p[j] >= nums[i]) {
            return false;
        }
        nums[i] -= p[j];
    }
    return true;
}
