Problem: There are N cells arranged in a row, numbered 1, 2, \ldots, N from left to right.

Tak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.

You are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \leq i \leq r.

* When you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.



To help Tak, find the number of ways to go to Cell N, modulo 998244353.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \min(N, 10)
* 1 \leq L_i \leq R_i \leq N
* [L_i, R_i] and [L_j, R_j] do not intersect (i \neq j)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
L_1 R_1
L_2 R_2
:
L_K R_K


Output

Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.

Examples

Input

5 2
1 1
3 4


Output

4


Input

5 2
3 3
5 5


Output

0


Input

5 1
1 2


Output

5


Input

60 3
5 8
1 3
10 15


Output

221823067

Solution (in JAVA):

Solution:
import java.util.*;

public class Main {
  static Scanner in = new Scanner(System.in);
  static List<Integer> list = new ArrayList<>();
  static int[] dp;
  static int[] sum;
  static int n;
  static int m;
  static int[] le;
  static int[] ri;
  static final int mod = 998244353;
  public static void main(String[] args) {
    n = in.nextInt();
    m = in.nextInt();
    le = new int[m];
    ri = new int[m];
    for (int i = 0; i < m; i++) {
      le[i] = in.nextInt();
      ri[i] = in.nextInt();
    }

    dp = new int[n + 1];
    Arrays.fill(dp, 0);
    sum = new int[n + 1];
    Arrays.fill(sum, 0);
    dp[1] = sum [1] = 1;
    for (int i = 2; i <=n; i++) {
      for (int k = 0; k < m; k++) {
        dp[i] = (dp[i] + get(i - ri[k], i - le[k])) % mod;
      }
      sum[i] = (sum[i-1] + dp[i]) % mod;
    }
    System.out.println(dp[n]);
  }

  private static int get(int x, int y) {
    if (y < 0) {
      y = 0;
    }
    if (x <= 0) {
      x = 1;
    }
    return ((sum[y] - sum[x - 1]) % mod + mod) % mod;
  }
}