Problem:
Score : 400 points

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.

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.

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.

Solution in Ruby (2.7.1) (judge verdict: Accepted)

N, K = gets.split.map(&:to_i)
LR = Array.new K
K.times do |i|
    LR[i] = gets.split.map(&:to_i)
end
LRS = LR.sort_by{|x| x[0]}
MOD=998244353


dp = Array.new N+1
dpSum = Array.new N+1
dp[0] = 0
dp[1] = 1
dpSum[0] = 0
dpSum[1] = 1
2.upto(N) do |n|
    cnt = 0
    LRS.each do |lr|
        l = lr[0]
        break if l > n
        r = lr[1]
        if r > n - 1
            r = n - 1
        end
        if l == r
            cnt += dp[n-l]
        else
            cnt += dpSum[n-l] - dpSum[n-r-1]
        end
    end
    dp[n] = cnt % MOD
    dpSum[n] = (dpSum[n-1] + cnt) % MOD
end

puts dp[N] % MOD