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>
const int MOD = 998244353;
using namespace std;
const int SIZE = 200010;
int L[SIZE],R[SIZE];
long long dp[SIZE];
long long sum[SIZE]; // sum[i] 代表 dp[1]+...+dp[i]
int get(int l,int r){
    if(l<=1)l=1;
    if(l>r)return 0;
    return ((sum[r]-sum[l-1])%MOD+MOD)%MOD;
}
int main() {
    int N,K;
    cin>>N>>K;
    for(int i=1;i<=K;i++){
        cin>>L[i]>>R[i];
    }
    dp[1]=sum[1]=1;
    for(int i=2;i<=N;i++){
        for(int j=1;j<=K;j++){
            dp[i] = (dp[i] + get(i-R[j],i-L[j])) % MOD;
        }
        sum[i] = (sum[i-1] + dp[i]) %MOD;
    }
    cout<< dp[N] << endl;
    return 0;
}