Problem: 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.

Examples

Input

5 2
1 1
3 4


Output

4


Input

5 2
3 3
5 5


Output

0


Input

5 1
1 2


Output

5


Input

60 3
5 8
1 3
10 15


Output

221823067

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class Main {
	static void solve() {
		int n = ni(), k = ni();
		long[] dp = new long[n+1];
		dp[0] = 1;
		int[][] a = na(k, 2);
		long[] p = new long[n+1];
		for(int i=0;i<n;i++) {
			dp[i] = plus(dp[i], p[i]);
			for(int j=0;j<k;j++) {
				int l = a[j][0], r = a[j][1];
				if(l + i >= n)continue;
				p[l+i] = plus(p[i+l], dp[i]);
				r = min(r + i, n-1);
				p[r+1] = sub(p[r+1], dp[i]);
			}
			p[i + 1] += p[i];
			p[i + 1] %= mod;
		}
		
		out.println(dp[n-1]);
	}	

	//constants
	static final int inf = Integer.MAX_VALUE / 2;
	static final long linf = Long.MAX_VALUE / 3;
	static final double dinf = Double.MAX_VALUE / 3;
	static final long mod = 998244353;
	static final int[] dx = { -1, 0, 1, 0 }, dy = { 0, -1, 0, 1 }, dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final double eps = 1e-10;
	
	//libraries
	static long[] cum(int a[]) {
		long[] cum = new long[a.length + 1];
		for(int i=0;i<a.length;i++) cum[i+1] = cum[i] + a[i];
		return cum;
	}
	static long[] cum(long a[]) {
		long[] cum = new long[a.length + 1];
		for(int i=0;i<a.length;i++) cum[i+1] = cum[i] + a[i];
		return cum;
	}
	static void reverse(int ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(long ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(double ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(char ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static String getReverse(String s) {
		StringBuilder sb = new StringBuilder(s);
		return sb.reverse().toString();
	}
	static <T> void reverse(T[] ar) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			T t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static int[] concat(int x, int arr[]) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}
	static int[] concat(int arr[], int x) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static long[] concat(long x, long arr[]) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}
	static long[] concat(long arr[], long x) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static char[] concat(char x, char arr[]) {
		char ret[] = new char[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static char[] concat(char arr[], char x) {
		char ret[] = new char[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static int max(int x, int y) {
		return Math.max(x, y);
	}
	static int min(int x, int y) {
		return Math.min(x, y);
	}
	static int max(int x, int y, int z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static int min(int x, int y, int z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static long max(long x, long y) {
		return Math.max(x, y);
	}
	static long min(long x, long y) {
		return Math.min(x, y);
	}
	static long max(long x, long y, long z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static long min(long x, long y, long z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static double max(double x, double y) {
		return Math.max(x, y);
	}
	static double min(double x, double y) {
		return Math.min(x, y);
	}
	static double max(double x, double y, double z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static double min(double x, double y, double z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static void sort(int[] ar) {
		Arrays.sort(ar);
	}
	static void sort(long[] ar) {
		Arrays.sort(ar);
	}
	static void sort(double[] ar) {
		Arrays.sort(ar);
	}
	static void sort(char[] ar) {
		Arrays.sort(ar);
	}
	static void rsort(int[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(long[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(double[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(char[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void fill(int arr[], int x) {
		Arrays.fill(arr, x);
	}
	static void fill(long arr[], long x) {
		Arrays.fill(arr, x);
	}
	static void fill(boolean arr[], boolean x) {
		Arrays.fill(arr, x);
	}
	static void fill(double arr[], double x) {
		Arrays.fill(arr, x);
	}
	static void fill(int arr[][], int x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(long arr[][], long x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(double arr[][], double x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(boolean arr[][], boolean x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	//MOD culc
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}
	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}
	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}
	//input
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	private static int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}
	private static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}
	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}
	@SuppressWarnings("unused")
	private static double nd() {
		return Double.parseDouble(ns());
	}
	@SuppressWarnings("unused")
	private static char nc() {
		return (char) skip();
	}
	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	@SuppressWarnings("unused")
	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}
	@SuppressWarnings("unused")
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	@SuppressWarnings("unused")
	private static long[] nla(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}
	@SuppressWarnings("unused")
	private static int[][] na(int n, int m){
		int[][] res = new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				res[i][j] = ni();
			}
		}
		return res;
	}
	@SuppressWarnings("unused")
	private static long[][] nla(int n, int m){
		long[][] res = new long[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				res[i][j] = nl();
			}
		}
		return res;
	}
	private static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	private static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
}