Problem Statement

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.

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.

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.

Sample Input 1

5 2
1 1
3 4

Sample Output 1

4

The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = { 1, 3, 4 } holds.
There are 4 possible ways to get to Cell 5:

• $1 \to$ $2 \to$ $3 \to$ $4 \to$ 5,
• $1 \to$ $2 \to$ 5,
• $1 \to$ $4 \to$ 5 and
• $1 \to$ 5.

Sample Input 2

5 2
3 3
5 5

Sample Output 2

0

Because S = { 3, 5 } holds, you cannot reach to Cell 5.
Print 0.

Sample Input 3

5 1
1 2

Sample Output 3

5

Sample Input 4

60 3
5 8
1 3
10 15

Sample Output 4

221823067

Note that you have to print the answer modulo 998244353.

见题面 Input 部分

见题面 Output 部分