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 <bits/stdc++.h>
using namespace std;

const long long mod = 998244353;

int main() {
  long long n;
  int k;
  cin >> n >> k;
  vector<pair<int, int>> range;
  for ( int i = 0; i < k; i++ ) {
    int l, r;
    cin >> l >> r;
    range.push_back({l, r+1});
  }

  vector<long long> dp(n);
  dp[0] = 1;
  for ( int i = 0; i < n; i++ ) {
    if ( i > 1 ) { dp[i] += dp[i-1]; dp[i] %= mod; }
    for ( int j = 0; j < k; j++ ) {
      int l, r;
      tie(l, r) = range[j];
      if ( i+l < n ) { dp[i+l] += dp[i]; dp[i+l] %= mod; }
      if ( i+r < n ) { dp[i+r] -= dp[i]; dp[i+r] += mod; dp[i+r] %= mod; }
    }
  }

  cout << dp[n-1] << endl;
  return 0;
}