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;

int MOD(int a, int b){
  int x = a % b;
  if(x >= 0)
    return (x);
  else
    return (x + b);
}

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