Zigu Zagu

1000ms

262144K

Description:

You have a binary string $$$a$$$ of length $$$n$$$ consisting only of digits $$$0$$$ and $$$1$$$.

You are given $$$q$$$ queries. In the $$$i$$$-th query, you are given two indices $$$l$$$ and $$$r$$$ such that $$$1 \le l \le r \le n$$$.

Let $$$s=a[l,r]$$$. You are allowed to do the following operation on $$$s$$$:

Choose two indices $$$x$$$ and $$$y$$$ such that $$$1 \le x \le y \le |s|$$$. Let $$$t$$$ be the substring $$$t = s[x, y]$$$. Then for all $$$1 \le i \le |t| - 1$$$, the condition $$$t_i \neq t_{i+1}$$$ has to hold. Note that $$$x = y$$$ is always a valid substring.
Delete the substring $$$s[x, y]$$$ from $$$s$$$.

For each of the $$$q$$$ queries, find the minimum number of operations needed to make $$$s$$$ an empty string.

Note that for a string $$$s$$$, $$$s[l,r]$$$ denotes the subsegment $$$s_l,s_{l+1},\ldots,s_r$$$.

Input:

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n, q \le 2 \cdot 10 ^ 5$$$) — the length of the binary string $$$a$$$ and the number of queries respectively.

The second line contains a binary string $$$a$$$ of length $$$n$$$ ($$$a_i \in \{0, 1\}$$$).

Each of the next $$$q$$$ lines contains two integers $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le n$$$) — representing the substring of each query.

Output:

Print $$$q$$$ lines, the $$$i$$$-th line representing the minimum number of operations needed for the $$$i$$$-th query.

Sample Input:

Sample Output:

1
3
2

Sample Input:

Sample Output:

4
2
3

Note:

In the first test case,

The substring is $$$\texttt{101}$$$, so we can do one operation to make the substring empty.
The substring is $$$\texttt{11011}$$$, so we can do one operation on $$$s[2, 4]$$$ to make $$$\texttt{11}$$$, then use two more operations to make the substring empty.
The substring is $$$\texttt{011}$$$, so we can do one operation on $$$s[1, 2]$$$ to make $$$\texttt{1}$$$, then use one more operation to make the substring empty.

Informação

Provedor Codeforces

Código CF1672H