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:
# 累積和を用いたdpの高速か

n, k = map(int, input().split())
mod = 998244353

lr_list = [list(map(int, input().split())) for _ in range(k)]

dp = [0] * (n + 1)
dp[1] = 1
sdp = [0] * (n + 1)
sdp[1] = 1
for i in range(2, n + 1):
    for j in range(k):
        right = max(0, i - lr_list[j][0])
        left = max(0, i - lr_list[j][1] - 1)
        dp[i] = (dp[i] + sdp[right] - sdp[left]) % mod
    sdp[i] = sdp[i - 1] + dp[i]

print(dp[n])