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Mammali's Way Out - Repovive Starter Round 6 | Repovive

19E. Mammali's Way Out

2500 pts1s256 MB

You are given an array $a$ of length $n$ , indexed from $1$ to $n$ . Every element of the array is either $+1$ or $-1$ . The array is represented by a string $s$ , where $s_i$ is + if $a_i=+1$ , and - if $a_i=-1$ .

An experiment can start at any position $i$ . Before every experiment, the array is restored to its initial state.

In the $i$ -th experiment, Mammali starts at position $i$ . While he is inside the array, suppose that his current position is $p$ and let $x=a_p$ . He performs the following actions:

he moves to position $p+x$ ;
$a_p$ is replaced by $-a_p$ , where $p$ is the position he just left.

In other words, the move uses the value of the position before its sign is reversed.

If Mammali reaches position $0$ , he exits from the left. If he reaches position $n+1$ , he exits from the right.

You are given $q$ queries. In the $j$ -th query, Mammali separately performs one experiment from every starting position $i$ such that $l_j \le i \le r_j$ . Determine how many of these experiments end with Mammali exiting from the left.

Queries do not change the array, and every experiment is independent of all other experiments.

Constraints

$1 \le n,q \le 2 \times 10^5$
$|s|=n$
$s_i$ is either + or -
$1 \le l_i \le r_i \le n$

Input

The first line contains two integers $n$ and $q$ .

The second line contains the string $s$ .

Each of the next $q$ lines contains two integers $l_i$ and $r_i$ , describing a query.

Output

For each query, output one integer: the number of starting positions in its range from which Mammali exits from the left.

Samples

Input

Explanation

Starting from position $1$ , the states after successive moves are:

position $2$ , string “---+”;
position $1$ , string “-+-+”;
position $0$ , string “++-+”.

Thus, Mammali exits from the left.

Starting from position $3$ , the states after successive moves are:

position $2$ , string “+-++”;
position $1$ , string “++++”;
position $2$ , string “-+++”;
position $3$ , string “--++”;
position $4$ , string “---+”;
position $5$ , string “----”.

Thus, Mammali exits from the right. The other two experiments can be followed in the same way.

In fact, starts $1$ and $2$ exit left, while starts $3$ and $4$ exit right. Therefore, the four query answers are $2$ , $2$ , $0$ , and $1$ .

Output

Input

5 3
-++--
1 5
2 4
4 5

Explanation

Starting from position $2$ , the states after successive moves are:

position $3$ , string “--+--”;
position $4$ , string “-----”;
position $3$ , string “---+-”;
position $2$ , string “--++-”;
position $1$ , string “-+++-”;
position $0$ , string “++++-”.

Thus, Mammali exits from the left.

Starting from position $5$ , the states after successive moves are:

position $4$ , string “-++-+”;
position $3$ , string “-++++”;
position $4$ , string “-+-++”;
position $5$ , string “-+--+”;
position $6$ , string “-+---”.

Thus, Mammali exits from the right. The other experiments can be followed in the same way.

The experiments starting at positions $1$ , $2$ , and $3$ exit left. The experiments starting at positions $4$ and $5$ exit right. Hence, all five positions contain three left exits, positions $2$ through $4$ contain two, and positions $4$ through $5$ contain none.

Output

3
2
0

An experiment can start at any position $i$ . Before every experiment, the array is restored to its initial state.

In the $i$ -th experiment, Mammali starts at position $i$ . While he is inside the array, suppose that his current position is $p$ and let $x=a_p$ . He performs the following actions:

he moves to position $p+x$ ;
$a_p$ is replaced by $-a_p$ , where $p$ is the position he just left.

In other words, the move uses the value of the position before its sign is reversed.

If Mammali reaches position $0$ , he exits from the left. If he reaches position $n+1$ , he exits from the right.

Queries do not change the array, and every experiment is independent of all other experiments.

$1 \le n,q \le 2 \times 10^5$
$|s|=n$
$s_i$ is either + or -
$1 \le l_i \le r_i \le n$

The first line contains two integers $n$ and $q$ .

The second line contains the string $s$ .

Each of the next $q$ lines contains two integers $l_i$ and $r_i$ , describing a query.

Starting from position $1$ , the states after successive moves are:

position $2$ , string “---+”;
position $1$ , string “-+-+”;
position $0$ , string “++-+”.

Thus, Mammali exits from the left.

Starting from position $3$ , the states after successive moves are:

position $2$ , string “+-++”;
position $1$ , string “++++”;
position $2$ , string “-+++”;
position $3$ , string “--++”;
position $4$ , string “---+”;
position $5$ , string “----”.

Thus, Mammali exits from the right. The other two experiments can be followed in the same way.

In fact, starts $1$ and $2$ exit left, while starts $3$ and $4$ exit right. Therefore, the four query answers are $2$ , $2$ , $0$ , and $1$ .

Starting from position $2$ , the states after successive moves are:

position $3$ , string “--+--”;
position $4$ , string “-----”;
position $3$ , string “---+-”;
position $2$ , string “--++-”;
position $1$ , string “-+++-”;
position $0$ , string “++++-”.

Thus, Mammali exits from the left.

Starting from position $5$ , the states after successive moves are:

position $4$ , string “-++-+”;
position $3$ , string “-++++”;
position $4$ , string “-+-++”;
position $5$ , string “-+--+”;
position $6$ , string “-+---”.

Thus, Mammali exits from the right. The other experiments can be followed in the same way.

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19E. Mammali's Way Out

Constraints

Input

Output

Samples

19E. Mammali's Way Out

Constraints

Input

Output

Samples