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 PYTHON3):

Solution:
mod = 998244353
n,k = map(int,input().split())
K = [list(map(int,input().split())) for i in range(k)]

dp = [0]*(n+1)
dp[0] = 1
dp2 = [0]*(n+1)
for i in range(n):
    dp2[i] = (dp2[i]+dp2[i-1])%mod
    dp[i] = (dp[i]+dp2[i])%mod
    for l,r in K:
        dp2[min(i+l,n)] = (dp2[min(i+l,n)]+dp[i])%mod
        dp2[min(i+r+1,n)] = (dp2[min(i+r+1,n)]-dp[i])%mod
print(dp[n-1]%mod)