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:
N,K = map(int, input().split())
LRs = []
P = 998244353
for _ in range(K):
  l,r = map(int, input().split())
  LRs.append((l,r))
  
memo = [0]*(N+2)
memo[1] = 1
memo[2] = -1
rlt = [0]*(N+2)
rlt[1] = 1


for i in range(1,N+1):
  for t in LRs:
    l = min(t[0]+i,N+1)
    r = min(t[1]+i+1,N+1)
    memo[l] = memo[l]+rlt[i]
    memo[r] = memo[r]-rlt[i]
  rlt[i+1] = (rlt[i]+memo[i+1])%P
  
print(rlt[N])