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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0].split(" ")[0]);
    const K = parseInt(arg[0].split(" ")[1]);
    const LR = arg.slice(1, N + 1).map(n=>n.split(" ").map(l=>parseInt(l)));
    
    const steps = arg[1].split(" ").map(n=>parseInt(n));
    const map = [...Array(N+1)].fill(0);
    
    let S = [];
    
    // 和集合
    for(let i=0; i<K; i++) {
        const L = LR[i][0];
        const R = LR[i][1];
        
        map[L]++;
        map[R+1]--;
    }
    
    let imosFlg = 0;
    
    for(let i=0; i<N; i++) {
        if(map[i] === 1) imosFlg++;
        if(map[i] === -1) imosFlg--;
        
        if(imosFlg) {
            S.push(i);
        }
    }
    
    // console.log(map);
    // console.log(S);
    // console.log("hage")
    
    const dp = [...Array(N)].fill(Infinity);
    const NS = S.length;
    
    dp[0] = 1;
    
    for(let i=1; i<N; i++) {
        //let temp = Infinity;
        
        // for(let j=1; j<=K; j++) {
        //     if(i-j >= 0) {
        //         temp = Math.min(temp, dp[i-j] + Math.abs(steps[i] - steps[i-j]));
        //     }
        // }

        let temp = 0;
        
        for(let j=0; j<NS; j++) {
            const hoge = S[j];
            //console.log("hoge:" + hoge)
            
            if(i-hoge >= 0 && dp[i - hoge] > 0 && dp[i-hoge] !== Infinity) {
                temp += dp[i-hoge] % 998244353;
            }
            
            if(i-hoge < 0) break;
        }
        
        dp[i] = temp % 998244353;
        // console.log("dp[i]:" + dp[i]);
        // console.log("-------")
    }
    
    // console.log(dp)
    
    console.log(dp[N-1] % 998244353);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));