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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;

class LazySegTree<S, F> {
	final int MAX;
	
	final int N;
	final int Log;
	final java.util.function.BinaryOperator<S> Op;
	final S E;
	final java.util.function.BiFunction<F, S, S> Mapping;
	final java.util.function.BinaryOperator<F> Composition;
	final F Id;
	
	final S[] Dat;
	final F[] Laz;
	
	@SuppressWarnings("unchecked")
	public LazySegTree(int n, java.util.function.BinaryOperator<S> op, S e, java.util.function.BiFunction<F, S, S> mapping, java.util.function.BinaryOperator<F> composition, F id) {
		this.MAX = n;
		int k = 1;
		while (k < n) k <<= 1;
		this.N = k;
		this.Log = Integer.numberOfTrailingZeros(N);
		this.Op = op;
		this.E = e;
		this.Mapping = mapping;
		this.Composition = composition;
		this.Id = id;
		this.Dat = (S[]) new Object[N << 1];
		this.Laz = (F[]) new Object[N];
		java.util.Arrays.fill(Dat, E);
		java.util.Arrays.fill(Laz, Id);
	}
	
	public LazySegTree(S[] dat, java.util.function.BinaryOperator<S> op, S e, java.util.function.BiFunction<F, S, S> mapping, java.util.function.BinaryOperator<F> composition, F id) {
		this(dat.length, op, e, mapping, composition, id);
		build(dat);
	}
	
	private void build(S[] dat) {
		int l = dat.length;
		System.arraycopy(dat, 0, Dat, N, l);
		for (int i = N - 1; i > 0; i--) {
			Dat[i] = Op.apply(Dat[i << 1 | 0], Dat[i << 1 | 1]);
		}
	}
	
	private void push(int k) {
		if (Laz[k] == Id) return;
		int lk = k << 1 | 0, rk = k << 1 | 1;
		Dat[lk] = Mapping.apply(Laz[k], Dat[lk]);
		Dat[rk] = Mapping.apply(Laz[k], Dat[rk]);
		if (lk < N) Laz[lk] = Composition.apply(Laz[k], Laz[lk]);
		if (rk < N) Laz[rk] = Composition.apply(Laz[k], Laz[rk]);
		Laz[k] = Id;
	}
	
	private void pushTo(int k) {
		for (int i = Log; i > 0; i--) push(k >> i);
	}
	
	private void pushTo(int lk, int rk) {
		for (int i = Log; i > 0; i--) {
			if (((lk >> i) << i) != lk) push(lk >> i);
			if (((rk >> i) << i) != rk) push(rk >> i);
		}
	}
	
	private void updateFrom(int k) {
		k >>= 1;
			while (k > 0) {
				Dat[k] = Op.apply(Dat[k << 1 | 0], Dat[k << 1 | 1]);
				k >>= 1;
			}
	}
	
	private void updateFrom(int lk, int rk) {
		for (int i = 1; i <= Log; i++) {
			if (((lk >> i) << i) != lk) {
				int lki = lk >> i;
			Dat[lki] = Op.apply(Dat[lki << 1 | 0], Dat[lki << 1 | 1]);
			}
			if (((rk >> i) << i) != rk) {
				int rki = (rk - 1) >> i;
			Dat[rki] = Op.apply(Dat[rki << 1 | 0], Dat[rki << 1 | 1]);
			}
		}
	}
	
	public void set(int p, S x) {
		exclusiveRangeCheck(p);
		p += N;
		pushTo(p);
		Dat[p] = x;
		updateFrom(p);
	}
	
	public S get(int p) {
		exclusiveRangeCheck(p);
		p += N;
		pushTo(p);
		return Dat[p];
	}
	
	public S prod(int l, int r) {
		if (l > r) {
			throw new IllegalArgumentException(
					String.format("Invalid range: [%d, %d)", l, r)
					);
		}
		inclusiveRangeCheck(l);
		inclusiveRangeCheck(r);
		if (l == r) return E;
		l += N; r += N;
		pushTo(l, r);
		S sumLeft = E, sumRight = E;
		while (l < r) {
			if ((l & 1) == 1) sumLeft = Op.apply(sumLeft, Dat[l++]);
			if ((r & 1) == 1) sumRight = Op.apply(Dat[--r], sumRight);
			l >>= 1; r >>= 1;
		}
		return Op.apply(sumLeft, sumRight);
	}
	
	public S allProd() {
		return Dat[1];
	}
	
	public void apply(int p, F f) {
		exclusiveRangeCheck(p);
		p += N;
		pushTo(p);
		Dat[p] = Mapping.apply(f, Dat[p]);
		updateFrom(p);
	}
	
	public void apply(int l, int r, F f) {
		if (l > r) {
			throw new IllegalArgumentException(
					String.format("Invalid range: [%d, %d)", l, r)
					);
		}
		inclusiveRangeCheck(l);
		inclusiveRangeCheck(r);
		if (l == r) return;
		l += N; r += N;
		pushTo(l, r);
		for (int l2 = l, r2 = r; l2 < r2;) {
			if ((l2 & 1) == 1) {
				Dat[l2] = Mapping.apply(f, Dat[l2]);
				if (l2 < N) Laz[l2] = Composition.apply(f, Laz[l2]);
				l2++;
			}
			if ((r2 & 1) == 1) {
				r2--;
				Dat[r2] = Mapping.apply(f, Dat[r2]);
				if (r2 < N) Laz[r2] = Composition.apply(f, Laz[r2]);
			}
			l2 >>= 1; r2 >>= 1;
		}
		updateFrom(l, r);
	}
	
	public int maxRight(int l, java.util.function.Predicate<S> g) {
		inclusiveRangeCheck(l);
		if (!g.test(E)) {
			throw new IllegalArgumentException("Identity element must satisfy the condition.");
		}
		if (l == MAX) return MAX;
		l += N;
		pushTo(l);
		S sum = E;
		do {
			l >>= Integer.numberOfTrailingZeros(l);
				if (!g.test(Op.apply(sum, Dat[l]))) {
					while (l < N) {
						push(l);
						l = l << 1;
						if (g.test(Op.apply(sum, Dat[l]))) {
							sum = Op.apply(sum, Dat[l]);
							l++;
						}
					}
					return l - N;
				}
				sum = Op.apply(sum, Dat[l]);
				l++;
		} while ((l & -l) != l);
		return MAX;
	}
	
	public int minLeft(int r, java.util.function.Predicate<S> g) {
		inclusiveRangeCheck(r);
		if (!g.test(E)) {
			throw new IllegalArgumentException("Identity element must satisfy the condition.");
		}
		if (r == 0) return 0;
		r += N;
		pushTo(r - 1);
		S sum = E;
		do {
			r--;
			while (r > 1 && (r & 1) == 1) r >>= 1;
						if (!g.test(Op.apply(Dat[r], sum))) {
							while (r < N) {
								push(r);
								r = r << 1 | 1;
								if (g.test(Op.apply(Dat[r], sum))) {
									sum = Op.apply(Dat[r], sum);
									r--;
								}
							}
							return r + 1 - N;
						}
						sum = Op.apply(Dat[r], sum);
		} while ((r & -r) != r);
		return 0;
	}
	
	private void exclusiveRangeCheck(int p) {
		if (p < 0 || p >= MAX) {
			throw new IndexOutOfBoundsException(
					String.format("Index %d is not in [%d, %d).", p, 0, MAX)
					);
		}
	}
	
	private void inclusiveRangeCheck(int p) {
		if (p < 0 || p > MAX) {
			throw new IndexOutOfBoundsException(
					String.format("Index %d is not in [%d, %d].", p, 0, MAX)
					);
		}
	}
}

public class Main {
	static void solve() {
		int n = ni(), k = ni();
		var dat = new S[3 * n];
		for(int i=0;i<3 * n;i++) dat[i] = new S(0, 1);
		LazySegTree<S, F> seg = new LazySegTree<>(dat, S::op, S.E, Main::map, F::composite, F.I);
		seg.set(0, new S(1, 1));
		var a = na(k, 2);
		for(int i=0;i<n;i++) {
			for(int j=0;j<k;j++) {
				int l = a[j][0], r = a[j][1] + 1;
				l += i; r += i;
				seg.apply(l, r, new F(seg.get(i).v));
			}
		}
		out.println(seg.get(n-1).v);
	}	
	
	static S map(F f, S s) {
		return new S((s.v + f.v * s.size) % mod, s.size);
	}
	
	static class S{
		long v;
		int size;
		public S(long v, int size) {
			super();
			this.v = v;
			this.size = size;
		}
		static final S E = new S(0, 0);
		
		static S op(S l, S r) {
			return new S((l.v + r.v) % mod, l.size + r.size);
		}
	}
	
	static class F{
		long v;

		public F(long v) {
			super();
			this.v = v;
		}
		
		static final F I = new F(0);
		
		static F composite(F f, F g) {
			return new F(( f.v + g.v ) % mod);
		}
	}
	
	//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();
		}
	}
}