<p>You are given an <code>m x n</code> binary matrix <code>grid</code> where each cell is either <code>0</code> (empty) or <code>1</code> (occupied).</p>

<p>You are then given stamps of size <code>stampHeight x stampWidth</code>. We want to fit the stamps such that they follow the given <strong>restrictions</strong> and <strong>requirements</strong>:</p>

<ol>
	<li>Cover all the <strong>empty</strong> cells.</li>
	<li>Do not cover any of the <strong>occupied</strong> cells.</li>
	<li>We can put as <strong>many</strong> stamps as we want.</li>
	<li>Stamps can <strong>overlap</strong> with each other.</li>
	<li>Stamps are not allowed to be <strong>rotated</strong>.</li>
	<li>Stamps must stay completely <strong>inside</strong> the grid.</li>
</ol>

<p>Return <code>true</code> <em>if it is possible to fit the stamps while following the given restrictions and requirements. Otherwise, return</em> <code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/03/ex1.png" style="width: 180px; height: 237px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0,0],[1,0,0,0],[1,0,0,0],[1,0,0,0],[1,0,0,0]], stampHeight = 4, stampWidth = 3
<strong>Output:</strong> true
<strong>Explanation:</strong> We have two overlapping stamps (labeled 1 and 2 in the image) that are able to cover all the empty cells.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/03/ex2.png" style="width: 170px; height: 179px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], stampHeight = 2, stampWidth = 2 
<strong>Output:</strong> false 
<strong>Explanation:</strong> There is no way to fit the stamps onto all the empty cells without the stamps going outside the grid.
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[r].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>grid[r][c]</code> is either <code>0</code> or <code>1</code>.</li>
	<li><code>1 &lt;= stampHeight, stampWidth &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def possibleToStamp(self, grid: List[List[int]], stampHeight: int, stampWidth: int) -> bool:
        m,n=len(grid),len(grid[0])
        #we scan the grid row by row, updating the heights of unoccupied and unstamped blocks for each row with two pointers, l and r, spaced width steps apart. We then greedily put stamps whenever the height and width of the unoccupied area allow, and check if any blank spots remain.
        #h store sthe height of consecutive unoccupied blocks for each column
        def acc_2d(grid):
            dp=[[0]*(n+1) for _ in range(m+1)]
            for r in range(m):
                for c in range(n):
                    dp[r + 1][c + 1] = (
                        dp[r + 1][c]           # Sum of elements to the left
                        + dp[r][c + 1]         # Sum of elements above
                        - dp[r][c]             # Subtract overlap region (top-left)
                        + grid[r][c]           # Add the current cell value
                    )
            
            return dp
        
        def SumRegion(r1,c1,r2,c2):
            return dp[r2+1][c2+1]-dp[r1][c2+1]-dp[r2+1][c1]+dp[r1][c1]
        dp=acc_2d(grid)
        diff=[[0]*(n+1) for _ in range(m+1)]
        for c in range(n-stampWidth+1):
            for r in range(m-stampHeight+1):
                if SumRegion(r,c,r+stampHeight-1,c+stampWidth-1)==0:
                    diff[r][c]+=1
                    diff[r][c+stampWidth]-=1
                    diff[r+stampHeight][c]-=1
                    diff[r+stampHeight][c+stampWidth]+=1
        dp2=acc_2d(diff)
        for r in  range(m):
            for c in  range(n):
                if dp2[r+1][c+1]==0 and grid[r][c]==0:
                    return False
        return True
65800