Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 2
1 1
3 4

Sample Output 1

4

The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = \{ 1, 3, 4 \} holds.

There are 4 possible ways to get to Cell 5:

1 \to 2 \to 3 \to 4 \to 5,

1 \to 2 \to 5,

1 \to 4 \to 5 and

1 \to 5.

Sample Input 2

5 2
3 3
5 5

Sample Output 2

0

Because S = \{ 3, 5 \} holds, you cannot reach to Cell 5.
Print 0.

Sample Input 3

5 1
1 2

Sample Output 3

5

Sample Input 4

60 3
5 8
1 3
10 15

Sample Output 4

221823067

Note that you have to print the answer modulo 998244353.

Solution in C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using Microsoft.VisualBasic;
using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.IO.Pipes;
using System.Linq;
using System.Net.Http.Headers;
using System.Security.Cryptography;

namespace AtCoder
{
	public class ABC
	{
		static public void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
			Solve(args);
			Console.Out.Flush();
		}

		//const int mod = 1000000007;  // 10^9+7
		const int mod = 998244353;
		static int Mod(long x, int m) { return (int)((x % m + m) % m); }
		static long Mod(long x, long m) { return (x % m + m) % m; }

		static public void Solve(string[] args)
		{
			//string s = Console.ReadLine();
			//int n = int.Parse(Console.ReadLine());
			//long x = long.Parse(Console.ReadLine());
			//int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] vs = Console.ReadLine().Split().Select(long.Parse).ToArray();

			int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int n = vs[0];
			int k = vs[1];
			List<int> s = new List<int>();
			for (int i = 0; i < k; i++) {
				vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
				for (int j = vs[0]; j <= vs[1]; j++) {
					s.Add(j);
				}
			}
			s.Sort();
			//System.Diagnostics.Debug.WriteLine(string.Join(" ", s));
			int[] dp = new int[n + 1];
			dp[1] = 1;
			for (int i = 2; i <= n; i++) {
				for (int j = 0; j < s.Count; j++) {
					if (0 < i - s[j]) {
						dp[i] += dp[i - s[j]];
						dp[i] %= mod;
					} else {
						break;
					}
				}
			}
			//System.Diagnostics.Debug.WriteLine(string.Join(" ", dp));
			Console.WriteLine(dp[n]);

		}
	}
}