<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>

import operator


class SegmentTree:
    def __init__(self, n, default_val=0, combine=operator.add):
        self._n = n
        self._default_val = default_val
        self._tree = [default_val] * (2 * n)
        self._combine = combine

    def set(self, i, x):
        i += self._n
        self._tree[i] = x
        i //= 2
        while i >= 1:
            self._tree[i] = self._combine(self._tree[2 * i], self._tree[2 * i + 1])
            i //= 2

    def query(self, l, r):
        l += self._n
        r += self._n
        res = self._default_val
        while l <= r:
            if l % 2 == 1:
                res = self._combine(res, self._tree[l])
                l += 1
            if r % 2 == 0:
                res = self._combine(res, self._tree[r])
                r -= 1
            l //= 2
            r //= 2
        return res

class Solution:
    def countKConstraintSubstrings(self, s: str, k: int, queries: List[List[int]]) -> List[int]:
        n = len(s)
        arr = SegmentTree(n)
        L = [None] * n
        l = 0
        cnt = [0] * 2
        for r in range(n):
            cnt[int(s[r])] += 1
            while min(cnt) > k:
                cnt[int(s[l])] -= 1
                l += 1
            L[r] = l
            arr.set(r, r - l + 1)
        res = []
        for l, r in queries:
            low, high = l, r + 1
            while high - low > 1:
                mid = (low + high) // 2
                if L[mid] < l:
                    low = mid
                else:
                    high = mid
            res.append(arr.query(high, r) + (low - l + 1) * (low - l + 2) // 2)
        return res

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