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# (Mono-csc 3.5.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
class d{
    public static void Main(){
        int div = 998244353;
        string[] str = Console.ReadLine().Split(' ');
        int n = int.Parse(str[0]);
        int k = int.Parse(str[1]);
        var list = new List<int>();
        for(int i=0; i<k; i++){
            int[] range = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            for(int j=range[0]; j<=range[1]; j++){
                list.Add(j);
            }
        }
        int[] pos = new int[n];
        pos[0] = 1;
        /*Queue<int> queue = new Queue<int>();
        queue.Enqueue(0);
        while(queue.Count > 0){
            int cur = queue.Dequeue();
            foreach(int v in list){
                if((v + cur) < n){
                    pos[v+cur] = (pos[v+cur] + pos[cur]) % div;
                    Console.WriteLine("----{0} {1}----",cur, v);
                    Console.WriteLine(string.Join(" ",pos));
                    queue.Enqueue(v+cur);
                }
            }

        }*/
        var sorted = new SortedSet<int>();
        sorted.Add(0);
        while(sorted.Count > 0){
            int cur = sorted.Min;
            sorted.Remove(cur);
            foreach(int v in list){
                if((v + cur) < n){
                    pos[v+cur] = (pos[v+cur] + pos[cur]) % div;
                    sorted.Add(v+cur);
                }
            }

        }
        //Console.WriteLine(string.Join(" ",pos));
        Console.WriteLine(pos[n-1]);
    }
}