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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)


from bisect import bisect_left,bisect

icase=0
if icase==0:
    n,k=map(int,input().split())

    s=[]
    for i in range(k):
        li,ri=list(map(int,input().split()))
        for i in range(li,ri+1):
            s.append(i)
elif icase==1:
    n,k=5,2
    s=[1, 3, 4]
elif icase==2:
    n,k=60,3    
    s=[5, 6, 7, 8, 1, 2, 3, 10, 11, 12, 13, 14, 15]

s.sort()

mod=998244353

dp=[0]*(n+1)
dp[1]=1

for i in range(1,n):
    ir=min(bisect(s,n-i)+1,n)
    for si in s[:ir]:
        j=i+si
        if j<=n:
            dp[j]=(dp[j]+dp[i])%mod
#    print(i,ir,dp)

print(dp[n])