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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC179D
{
    class Program
    {
        static long ans = 0;
        static long mod= 998244353;
        static void Main(string[] args)
        {
            string[] NK = Console.ReadLine().Split(' ');
            long N = long.Parse(NK[0]);
            int K = int.Parse(NK[1]);
            bool[] hantei = new bool[200001];
            long[] henka = new long[K * 2];
            for(int i = 0; i < K; i++)
            {
                string[] LR = Console.ReadLine().Split(' ');
                long L = long.Parse(LR[0]);
                long R = long.Parse(LR[1]);
                henka[i * 2] = L * -1;
                henka[i * 2 + 1] = R * -1;
                for(long j = L; j <= R; j++)
                {
                    hantei[j] = true;
                }
            }
            //Console.WriteLine(string.Join(" ", S));
            //Console.WriteLine(string.Join(" ", henka));
            long[] ans = new long[N];
            ans[0] = 1;
            //Console.WriteLine(string.Join(" ", ans));
            for (int i = 1; i < N; i++)
            {
                //Console.WriteLine(string.Join(" ", henka));
                if (i > 1)
                {
                    ans[i] = ans[i - 1];
                }
                for(int d = 0; d < K; d++)
                {
                    if (henka[d * 2]+1 >= 0)
                    {
                        ans[i] += ans[henka[d * 2]+1];
                        ans[i] %= mod;
                    }
                    if (henka[d * 2 + 1] >= 0)
                    {
                        ans[i] += mod-ans[henka[d * 2 + 1]];
                        ans[i] %= mod;
                    }
                    henka[d * 2] += 1;
                    henka[d * 2 + 1] += 1;
                }
            }
            //Console.WriteLine(string.Join(" ", ans));
            Console.WriteLine(ans[N-1]);
        }
    }
}