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;
using ll = long long;
constexpr ll MOD = 998244353;
int l[10], r[10];
// dp[i] = 範囲 [1, i] に到着する場合の数
ll dp[200001]={};
int main()
{
    ll n, k;
    cin >> n >> k;
    for(int i=0; i<k; ++i)cin >> l[i] >> r[i];
    dp[1]=1;
    for(int i=2; i<=n; ++i){
        dp[i] = dp[i-1];
        for(int j=0; j<k; ++j){
            int ll = max(1, i-r[j]);
            int rr = min(i-1, i-l[j]);
            if(ll<=rr){
                dp[i] += dp[rr] - dp[ll-1];
            }
        }
        dp[i] = (dp[i]%MOD + MOD)%MOD;
    }
    cout << (dp[n]-dp[n-1]+MOD)%MOD << endl;
    return 0;
}