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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

int main() {
  ll n,k;
  cin >> n >> k;
  vector<ll> dp(n);
  vector<ll> l(k);
  vector<ll> r(k);
  ll M=998244353;
  rep(i,k){
    cin >> l[i] >> r[i];
  }
  rep(i,n){
    if(i==0){
      dp[i]=1;
    }else{
      dp[i]=dp[i-1];
      rep(j,k){
        if (i-r[j]-1>=0){
          dp[i]+=dp[i-l[j]];
          dp[i]-=dp[i-r[j]-1];
        }else if(i-l[j]>=0){
          dp[i]+=dp[i-l[j]];
        }
      }
      dp[i]=(dp[i]+M)%M;
    }
  }
  ll res= (dp[n-1]-dp[n-2]+M)%M;
  cout << res << endl;
  return 0;
}