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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

type Range struct {
	begin int
	end   int
}

func main() {
	buf := make([]byte, 1024*1024)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)

	n := nextInt()
	k := nextInt()

	ranges := make([]Range, k)
	for i := 0; i < k; i++ {
		ranges[i].begin = nextInt()
		ranges[i].end = nextInt() + 1
	}

	fmt.Println(solve(n, k, ranges))
}

const M = 998244353

func solve(n int, k int, ranges []Range) int64 {
	dp := make([]int64, n)
	dp[0] = 1
	dp[1] = -1
	var cur int64 = 0

	for i := 0; i < n; i++ {
		cur = modM(cur + dp[i])

		if cur == 0 {
			continue
		}

		for j := 0; j < k; j++ {
			update(dp, n, i+ranges[j].begin, cur)
			update(dp, n, i+ranges[j].end, -cur)
		}
	}

	return cur
}

func update(dp []int64, n int, index int, cur int64) {
	if index < n {
		dp[index] = modM(dp[index] + cur)
	}
}

func modM(a int64) int64 {
	b := a % M
	if b < 0 {
		return b + M
	} else {
		return b
	}
}