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;
const int mod=998244353;
int n,k,f[200005]={0,1},d[200005]={0,1,-1};
struct node{int l,r;}a[15];
bool cmp(node a,node b){return a.l<b.r;}
int main(){
    cin>>n>>k;
    for(int i=1;i<=k;i++)cin>>a[i].l>>a[i].r;
    sort(a+1,a+1+k,cmp);
    for(int i=1;i<=n;i++){
        f[i]=(f[i-1]+d[i])%mod;
//        cout<<f[i]<<" "<<d[i]<<endl;
        if(f[i])for(int j=1;j<=k&&a[j].l+i<=n;j++){
            d[i+a[j].l]=(d[i+a[j].l]+f[i])%mod,d[i+a[j].r+1]=(d[i+a[j].r+1]-f[i])%mod;
//            cout<<i<<" "<<i+a[j].l<<" "<<i+a[j].r+1<<endl;
        }
    }
    cout<<(f[n]+mod)%mod<<endl;
    return 0;
}