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 <string>
#include <vector>
#include <algorithm>
#include <numeric>

using namespace std;
typedef long long ll;
const ll M = 998244353;

int main(){
  ll N,K;
  cin>> N >> K;
  ll L[K],R[K];
  //vector<ll> p;
  for(ll i=0;i<K;i++){
    cin >> L[i] >> R[i];
  }
  ll a[N+1];
  ll f[N+1];
  for(ll i=0;i<N+1;i++){
    f[i]=0;
    a[0]=0;
  }
  f[1] = 1;
  a[1] = 1;
  for(ll i=0;i<N+1;i++){
    for(ll j=0;j<K;j++){
      ll li = i-R[j];
      ll ri = i-L[j];
      if(ri<0) continue;
      if(li<1) li=1;
      f[i] += (a[ri] - a[li-1])%M;
    }
    a[i] = a[i-1]+f[i];
  }

  cout << f[N]%M << endl;
}