<p>You are given a 2D <code>matrix</code> of size <code>m x n</code>, consisting of non-negative integers. You are also given an integer <code>k</code>.</p>

<p>The <strong>value</strong> of coordinate <code>(a, b)</code> of the matrix is the XOR of all <code>matrix[i][j]</code> where <code>0 &lt;= i &lt;= a &lt; m</code> and <code>0 &lt;= j &lt;= b &lt; n</code> <strong>(0-indexed)</strong>.</p>

<p>Find the <code>k<sup>th</sup></code> largest value <strong>(1-indexed)</strong> of all the coordinates of <code>matrix</code>.</p>

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

<pre>
<strong>Input:</strong> matrix = [[5,2],[1,6]], k = 1
<strong>Output:</strong> 7
<strong>Explanation:</strong> The value of coordinate (0,1) is 5 XOR 2 = 7, which is the largest value.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[5,2],[1,6]], k = 2
<strong>Output:</strong> 5
<strong>Explanation:</strong> The value of coordinate (0,0) is 5 = 5, which is the 2nd largest value.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[5,2],[1,6]], k = 3
<strong>Output:</strong> 4
<strong>Explanation:</strong> The value of coordinate (1,0) is 5 XOR 1 = 4, which is the 3rd largest value.</pre>

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 1000</code></li>
	<li><code>0 &lt;= matrix[i][j] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= k &lt;= m * n</code></li>
</ul>

class KthLargest {
public:
    priority_queue<int , vector<int> , greater<int> > pq ; 
    int K;
    KthLargest(int k, vector<int> nums) {
        K=k;
        for(auto i:nums){
            pq.push(i);
        }
        while(pq.size()>k){
            pq.pop();
        }
    }
    
    void add(int val) {
        if(pq.size()<K){
            pq.push(val);
        }
        else{
            if(pq.top() < val){
                pq.pop();
                pq.push(val);
            }
        }
        // cout<<pq.size()<<" " << pq.top()<<endl ; 
    }

    int result(){
        if(pq.size()<K)return -1;
        return pq.top();
    }
};

class Solution {
public:
    int kthLargestValue(vector<vector<int>>& mat, int k) {
        vector<vector<int>> v = mat;

        KthLargest* q = new KthLargest(k , {});

        v[0][0]=mat[0][0];

        for(int i=0;i<v.size() ; i++){
            for(int j=1;j<v[0].size() ; j++){
                v[i][j] ^= v[i][j-1];
            }
        }
        for(int j=0;j<v[0].size();j++){
            q->add(v[0][j]);
        }
        for(int j=0;j<v[0].size() ; j++){
            for(int i=1;i<v.size() ; i++){
                v[i][j] ^= v[i-1][j];
                q->add(v[i][j]);
            }
        }


        // for(auto i:v){
        //     for(auto j:i)cout<<j<<' ';
        //     cout<<endl;
        // }

        return q->result() ;
    }
};
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