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: Accepted)

class SegmentTree:
    def __init__(self, n, op, e):
        self.n = 1 << (n - 1).bit_length()
        self.op = op
        self.e = e
        self.data = [e] * (2 * self.n)

    def update(self, k, v):
        k += self.n
        self.data[k] = v
        while k > 0:
            k >>= 1
            self.data[k] = self.op(self.data[2 * k], self.data[2 * k + 1])

    def query(self, left, right):
        left += self.n
        right += self.n
        l_res = self.e
        r_res = self.e
        while left < right:
            if left & 1:
                l_res = self.op(l_res, self.data[left])
                left += 1
            left >>= 1
            if right & 1:
                right -= 1
                r_res = self.op(self.data[right], r_res)
            right >>= 1
        return self.op(l_res, r_res)


MOD = 998244353
N, K, *LR = map(int, open(0).read().split())
segments = [(l, r) for l, r in zip(*[iter(LR)] * 2)]
st = SegmentTree(N + 1, lambda x, y: (x + y) % MOD, 0)
st.update(0, 1)
for i in range(1, N + 1):
    for l, r in segments:
        if i - l < 0:
            continue
        L = max(i - r, 0)
        R = i - l
        st.update(i, st.query(i, i + 1) + st.query(L, R + 1))
print(st.query(N - 1, N))