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: Wrong Answer)

function spilitInput(input, to_int) {
  if (typeof to_int === 'undefined') to_int = false;
  var splited = [];
  var rows = input.split('\n');
  for (var i = 0; i < rows.length; i += 1) {
    if (to_int) {
      splited.push(rows[i].split(' ').map(function(d){return parseInt(d,10);}));
    } else {
      splited.push(rows[i].split(' '));
    }
  }
  return splited;
}

function initDp(N, init_n) { return Array(N+2).fill(init_n); }
function chmin(a, b) { if (a > b) a = b; }
function chmax(a, b) { if (a < b) a = b; }

function Main(input) {
  var splited = spilitInput(input, true);
  var N = splited[0][0];
  var kouho = [];
  for (var i = 1; i < splited.length; i += 1) {
    if (kouho.indexOf(splited[i][0]) === -1) kouho.push(splited[i][0]);
    if (kouho.indexOf(splited[i][1]) === -1) kouho.push(splited[i][1]);
  }
    
  var dp = initDp(N, 0); // dpの初期化（要素数, 各要素の初期値）
  dp[0] = 1;
  
  for (var i = 1; i < N; i += 1) {
    for (var j = 0; j < kouho.length; j += 1) {
      if (i >= kouho[j]) dp[i] += dp[i - kouho[j]];
    }
    
    dp[i] %= 998244353; // AtCoderでよくある'XXXで割ってください'の数指定
  }

  console.log(dp[N-1]);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));