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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;
public class Main {
    public static void main(String [] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int K = sc.nextInt();
        long [] List = new long [N+1];
        Arrays.fill(List,0);
        Set<Integer> set = new HashSet<>();
        ArrayList<node> v = new ArrayList<>();
        node v2 = new node();
        v2.element(sc.nextInt(),sc.nextInt());
        v.add(v2);
        for(int i=1;i<K;i++){
            int L = sc.nextInt();
            int R = sc.nextInt();
            for(node vv:v){
                if(vv.l>L&&R>=vv.l&&R<=vv.r) vv.l = L;
                else if(L>=vv.l&&R>vv.r&&L<=vv.r) vv.r=R;
                else if(L<vv.l&&R>vv.r){
                    vv.l = L;
                    vv.r = R;
                }
                else{
                    node V = new node();
                    V.element(L,R);
                    v.add(V);
                    break;
                }
            }
        }
        for(node n:v) {
            for(int i=n.l;i<=n.r;i++){
                set.add(i);
                if(i+1<=N)List[i+1]=1;
            }
        }
        for(int i=2;i<N;i++){
            if(List[i]!=0){
                for(int j:set){
                    if(i+j<=N)List[i+j]=(List[i+j]+List[i])%998244353;
                    else break;
                }
            }
        }
        System.out.println(List[N]);
    }
    public static class node{
        int l,r;
        public void element(int l,int r){
            this.l = l;
            this.r = r;
        }
    }
}