Problem: 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.

Examples

Input

5 2
1 1
3 4


Output

4


Input

5 2
3 3
5 5


Output

0


Input

5 1
1 2


Output

5


Input

60 3
5 8
1 3
10 15


Output

221823067

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdint>

using namespace std;

int main() {
  const uint64_t mod = 998244353;
  uint64_t n, k;
  cin >> n >> k;
  uint64_t l[10];
  uint64_t r[10];
  for (uint64_t i = 0; i < k; ++i) {
    cin >> l[i] >> r[i];
  }
  uint64_t d[400020] = {0, 1, mod-1};
  uint64_t p = 1;
  for (uint64_t i = 1; i < n; ++i) {
    for (uint64_t j = 0; j < k; ++j) {
      d[i+l[j]] = (d[i+l[j]] + p) % mod;
      d[i+r[j]+1] = (d[i+r[j]+1] + mod - p) % mod;
    }
    p = (p + d[i+1]) % mod;
  }

  cout << p << endl;
}