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<vector>
using namespace std;
using ll = long long;

int main() {
  int N,K,i,j,MOD=998244353;
  cin>>N>>K;
  vector<int> L(K),R(K);
  for (i=0;i<K;i++) {
    cin>>L[i]>>R[i];
  }
  vector<ll> dp(N+1, 0), dps(N+1,0);
  dp[0]=0;dp[1]=1;
  dps[0]=0;dps[1]=1;
  for (i=2;i<=N;i++) {
    for (j=0;j<K;j++) {
      int r = i-L[j];
      int l = max(i-R[j],1);
      if (0<r) {
        dp[i] += (dps[r] - dps[l-1] + MOD) % MOD;
        dp[i] %= MOD;
      }
    }
    dps[i] = (dps[i-1] + dp[i]) % MOD;
  }
  cout<<dp[N]<<endl;
  return 0;
}