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.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説通りに実装したソースコード
 */
public class Main {

	private static final long MOD = 998_244_353L;

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), k = scanner.nextInt();
			long[] dp = new long[n + 2];
			Arrays.fill(dp, 0L);
			dp[0] = 1L;
			dp[2] = -1L;
			int[] l = new int[k], r = new int[k];
			IntStream.range(0, k).forEach(i -> {
				l[i] = scanner.nextInt();
				r[i] = scanner.nextInt();
			});
			IntStream.rangeClosed(1, n).forEach(i -> {
				dp[i] = (dp[i] + dp[i - 1]) % MOD;
				IntStream.range(0, k).filter(j -> i + l[j] <= n).forEach(j -> {
					dp[i + l[j]] = (dp[i + l[j]] + dp[i]) % MOD;
					dp[Math.min(n + 1, i + r[j] + 1)] = (dp[Math.min(n + 1, i + r[j] + 1)] - dp[i] + MOD) % MOD;
				});
			});
			System.out.println(dp[n]);
		}
	}
}