<p>You are given a <strong>binary</strong> string <code>s</code> and an integer <code>k</code>.</p>

<p>You are also given a 2D integer array <code>queries</code>, where <code>queries[i] = [l<sub>i</sub>, r<sub>i</sub>]</code>.</p>

<p>A <strong>binary string</strong> satisfies the <strong>k-constraint</strong> if <strong>either</strong> of the following conditions holds:</p>

<ul>
	<li>The number of <code>0</code>&#39;s in the string is at most <code>k</code>.</li>
	<li>The number of <code>1</code>&#39;s in the string is at most <code>k</code>.</li>
</ul>

<p>Return an integer array <code>answer</code>, where <code>answer[i]</code> is the number of <span data-keyword="substring-nonempty">substrings</span> of <code>s[l<sub>i</sub>..r<sub>i</sub>]</code> that satisfy the <strong>k-constraint</strong>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;0001111&quot;, k = 2, queries = [[0,6]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[26]</span></p>

<p><strong>Explanation:</strong></p>

<p>For the query <code>[0, 6]</code>, all substrings of <code>s[0..6] = &quot;0001111&quot;</code> satisfy the k-constraint except for the substrings <code>s[0..5] = &quot;000111&quot;</code> and <code>s[0..6] = &quot;0001111&quot;</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;010101&quot;, k = 1, queries = [[0,5],[1,4],[2,3]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[15,9,3]</span></p>

<p><strong>Explanation:</strong></p>

<p>The substrings of <code>s</code> with a length greater than 3 do not satisfy the k-constraint.</p>
</div>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
	<li><code>1 &lt;= k &lt;= s.length</code></li>
	<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>
	<li><code>queries[i] == [l<sub>i</sub>, r<sub>i</sub>]</code></li>
	<li><code>0 &lt;= l<sub>i</sub> &lt;= r<sub>i</sub> &lt; s.length</code></li>
	<li>All queries are distinct.</li>
</ul>

class Solution:
    def countKConstraintSubstrings(self, s: str, k: int, queries: List[List[int]]) -> List[int]:
        len_string = len(s)
        answer = [0] * len(queries)

        c = [0, 0]
        l = 0
        l2r = [0] * (len_string)
        l2r[0] = 1
        c[int(s[0])] += 1
        for n in range(1, len_string):
            c[int(s[n])] += 1
            # Move l
            while c[0] > k and c[1] > k:
                c[int(s[l])] -= 1
                l += 1
            l2r[n] = l2r[n - 1] + n - l + 1
        # print(l2r)

        c = [0, 0]
        r = len_string - 1
        r_bound = [0] * (len_string)
        r_bound[-1] = r
        c[int(s[-1])] += 1
        for n in range(len_string - 2, -1, -1):
            c[int(s[n])] += 1
            # Move l
            while c[0] > k and c[1] > k:
                c[int(s[r])] -= 1
                r -= 1
            r_bound[n] = r
        # print(r_bound)

        # "0101|01"
        #   ---|
        #    --|-
        #     -|--
        for i, q in enumerate(queries):
            [l, r] = q
            sep = min(r_bound[l], r)
            left = sep - l + 1
            left = left * (left + 1) // 2
            right = l2r[r] - l2r[sep]
            answer[i] = left + right
            # print((l, r, sep))
        return answer
74000