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 System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("5 2");
            WillReturn.Add("1 1");
            WillReturn.Add("3 4");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5 2");
            WillReturn.Add("3 3");
            WillReturn.Add("5 5");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("5 1");
            WillReturn.Add("1 2");
            //5
        }
        else if (InputPattern == "Input4") {
            WillReturn.Add("60 3");
            WillReturn.Add("5 8");
            WillReturn.Add("1 3");
            WillReturn.Add("10 15");
            //221823067
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    const int Hou = 998244353;
    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        SplitAct(InputList[0]);
        int N = wkArr[0];

        var DSet = new HashSet<int>();

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);

            int L = wkArr[0];
            int R = wkArr[1];
            for (int I = L; I <= R; I++) {
                DSet.Add(I);
            }
        }
        int[] AscDArr = DSet.OrderBy(pX => pX).ToArray();

        //場合の数[現在位置]
        int UB = N;
        int[] DPArr = new int[UB + 1];
        DPArr[1] = 1;

        for (int I = 1; I <= UB; I++) {
            if (DPArr[I] == 0) continue;
            foreach (int EachInt in AscDArr) {
                int NewInd = I + EachInt;
                if (UB < NewInd) break;
                DPArr[NewInd] += DPArr[I];
                DPArr[NewInd] %= Hou;
            }
        }
        Console.WriteLine(DPArr[UB]);
    }
}