<p>You are given an integer array <code>nums</code> and an integer <code>x</code>. In one operation, you can either remove the leftmost or the rightmost element from the array <code>nums</code> and subtract its value from <code>x</code>. Note that this <strong>modifies</strong> the array for future operations.</p>

<p>Return <em>the <strong>minimum number</strong> of operations to reduce </em><code>x</code> <em>to <strong>exactly</strong></em> <code>0</code> <em>if it is possible</em><em>, otherwise, return </em><code>-1</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,1,4,2,3], x = 5
<strong>Output:</strong> 2
<strong>Explanation:</strong> The optimal solution is to remove the last two elements to reduce x to zero.
</pre>

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

<pre>
<strong>Input:</strong> nums = [5,6,7,8,9], x = 4
<strong>Output:</strong> -1
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,2,20,1,1,3], x = 10
<strong>Output:</strong> 5
<strong>Explanation:</strong> The optimal solution is to remove the last three elements and the first two elements (5 operations in total) to reduce x to zero.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= x &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
private:
    vector<int> psum = vector<int>(1e5);
public:
    int minOperations(vector<int>& nums, int x) {
        int n = nums.size(), sum = 0, n_left, minmoves = n;

        psum[0] = nums[0];

        for(int i = 1; i < n; i++) {
            psum[i] = psum[i-1] + nums[i];
        }

        if (psum[n-1] < x) return -1;
        if (psum[n-1] == x) return n; 

        for(int i = n; i > 0 and sum <= x; i--) {
            if(i<n) sum += nums[i];

            if(x==sum){
                minmoves = min(minmoves, n-i);
                break;
            }

            auto ele = lower_bound(begin(psum), begin(psum)+n, x-sum);
            n_left = ele - begin(psum);
            if(*ele == x-sum and n_left != n){
                minmoves = min(minmoves, n_left + n - i + 1);
            } 
        }

        return minmoves == n ? -1 : minmoves;
    }
};

auto init = []() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    return 'c';
}();
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