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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

const MOD:isize = 998244353;
fn main() {
  input! {
    n: usize,
    k: usize,
    vals: [(usize, usize);k]
  }

  let mut dp: Vec<isize> = vec![0;n+1];
  let mut dp_sum: Vec<isize> = vec![0;n+1];
  dp[1] = 1;
  dp_sum[1] = 1;
  for i in 2..=n {
    for ii in 0..k {
      let (l, r) = vals[ii];
      let ri = if i <= l {
        continue
      } else {
        i - l
      };
      let li = if i <= r {
        0
      } else {
        i - r - 1
      };
      
      let mut v = (dp_sum[ri] - dp_sum[li]) % MOD;
      if v < 0 {
        v += MOD;
      }
      dp[i] += v;
      dp[i] %= MOD;
    }
    dp_sum[i] = (dp_sum[i-1] + dp[i]) % MOD;
  }
  println!("{}", dp[n]);
}