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;

int64_t Q=998244353;


int main() {
  int N,K;
  cin>>N>>K;
  vector<pair<int,int>> p(K);
  for(int i=0;i<K;i++){
    int a,b;
    cin>>a>>b;
    p[i]=make_pair(a,b);
  }
  sort(p.begin(),p.end());
  vector<int64_t> dp(N+1);
  vector<int64_t> rui(N+1);
  dp[1]=1;
  rui[1]=1;
  for(int i=2;i<=N;i++){
    int64_t A=0;
    for(int j=0;j<K;j++){
      int a,b;
      tie(a,b)=p[j];
      if(i<=a){
        break;
      }
      A+=rui[i-a]-rui[max(i-b-1,0)];
      A+=Q;
      A%=Q;
    }
    dp[i]=A;
    rui[i]=(dp[i]+rui[i-1])%Q;
  }
  cout<<dp[N]<<endl;
}