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;
#define lint long long
#define inf 100000000000000000
#define mod 998244353
#define MAX 1000005
#define pb push_back
#define vit vector<int>::iterator
typedef pair<lint,lint> pii;
lint L[MAX],R[MAX],P[MAX],DP[MAX];
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    lint n,k;
    cin>>n>>k;
    for(lint i=1;i<=k;i++) cin>>L[i]>>R[i];
    DP[n]=1;P[n]=1;
    for(lint i=n-1;i>=1;i--){
        for(lint j=1;j<=k;j++){
            DP[i]=(DP[i]+P[i+L[j]]-P[i+R[j]+1]+mod)%mod;
        }
        P[i]=(P[i+1]+DP[i])%mod;
    }
    cout<<DP[1];
    return 0;
}