Problem:
Score : 300 points

Problem Statement

We have N ID cards, and there are M gates.

We can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, ..., and R_i-th ID cards.

How many of the ID cards allow us to pass all the gates alone?

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i \leq R_i \leq N

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M

Output

Print the number of ID cards that allow us to pass all the gates alone.

Sample Input 1

4 2
1 3
2 4

Sample Output 1

2

Two ID cards allow us to pass all the gates alone, as follows:

The first ID card does not allow us to pass the second gate.

The second ID card allows us to pass all the gates.

The third ID card allows us to pass all the gates.

The fourth ID card does not allow us to pass the first gate.

Sample Input 2

10 3
3 6
5 7
6 9

Sample Output 2

1

Sample Input 3

100000 1
1 100000

Sample Output 3

100000

Solution in OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

let make_gate_list l r =
  let rec hoge l r =
    if l > r then
      []
    else
      l :: hoge (l + 1) r
  in
    hoge l r


let hikaku_lst lst1 lst2 =
  let hikaku n =
    List.filter (fun m -> n = m) lst2
  in
    List.map hikaku lst1 |> List.concat


let () = Scanf.scanf "%d %d\n" (fun n m ->
    let card_lst = make_gate_list 1 n in
    let rec loop i lst =
      if i = m then (*iは回数制限（最初のnに達したら終了）*)
      card_lst else
        let i = i + 1 in
        Scanf.scanf "%d %d\n" (fun l r ->
          let gate_list = make_gate_list l r in
          let ok_list = hikaku_lst gate_list lst in
          hikaku_lst ok_list (loop i ok_list)
        )
      in
    let lst = loop 0 card_lst in
     Printf.printf "%d" (List.length lst)
)