Problem: This is the hard version of the problem. The only difference between the easy version and the hard version is the constraints on n. You can only make hacks if both versions are solved.

A permutation of 1, 2, …, n is a sequence of n integers, where each integer from 1 to n appears exactly once. For example, [2,3,1,4] is a permutation of 1, 2, 3, 4, but [1,4,2,2] isn't because 2 appears twice in it.

Recall that the number of inversions in a permutation a_1, a_2, …, a_n is the number of pairs of indices (i, j) such that i < j and a_i > a_j.

Let p and q be two permutations of 1, 2, …, n. Find the number of permutation pairs (p,q) that satisfy the following conditions:

  * p is lexicographically smaller than q. 
  * the number of inversions in p is greater than the number of inversions in q. 



Print the number of such pairs modulo mod. Note that mod may not be a prime.

Input

The only line contains two integers n and mod (1≤ n≤ 500, 1≤ mod≤ 10^9).

Output

Print one integer, which is the answer modulo mod.

Example

Input


4 403458273


Output


17

Note

The following are all valid pairs (p,q) when n=4.

  * p=[1,3,4,2], q=[2,1,3,4], 
  * p=[1,4,2,3], q=[2,1,3,4], 
  * p=[1,4,3,2], q=[2,1,3,4], 
  * p=[1,4,3,2], q=[2,1,4,3], 
  * p=[1,4,3,2], q=[2,3,1,4], 
  * p=[1,4,3,2], q=[3,1,2,4], 
  * p=[2,3,4,1], q=[3,1,2,4], 
  * p=[2,4,1,3], q=[3,1,2,4], 
  * p=[2,4,3,1], q=[3,1,2,4], 
  * p=[2,4,3,1], q=[3,1,4,2], 
  * p=[2,4,3,1], q=[3,2,1,4], 
  * p=[2,4,3,1], q=[4,1,2,3], 
  * p=[3,2,4,1], q=[4,1,2,3], 
  * p=[3,4,1,2], q=[4,1,2,3], 
  * p=[3,4,2,1], q=[4,1,2,3], 
  * p=[3,4,2,1], q=[4,1,3,2], 
  * p=[3,4,2,1], q=[4,2,1,3]. 

Solution (in JAVA):

Solution:
//package round729;
import java.io.*;
import java.util.*;

public class E1 {
	InputStream is;
	FastWriter out;
	String INPUT = "";

	void solve()
	{
		int n = ni(), mod = ni();

		long ans = 0;
		long[] dp = new long[n*(n-1)/2+1];
		dp[0] = 1 % mod;
		long S = 0;
		for(int i = 1;i <= n-1;){

			long[] pre = new long[i*(i-1)/2+1];
			pre[0] = dp[0];
			for(int j = 0;j < i*(i-1)/2;j++){
				pre[j+1] = pre[j] + dp[j+1];
				if(pre[j+1] >= mod)pre[j+1] -= mod;
			}
			long[] cpre = new long[pre.length+1];
			for(int j = 0;j < pre.length;j++){
				cpre[j+1] = cpre[j] + pre[j];
				if(cpre[j+1] >= mod)cpre[j+1] -= mod;
			}
			long[] wpre = new long[pre.length+1];
			for(int j = 0;j < pre.length;j++){
				wpre[j+1] = wpre[j] + (long)j * pre[j];
				wpre[j+1] %= mod;
			}

//			S -= System.nanoTime();
			long s = 0;
			for(int j = 0;j < pre.length;j++){
				//				s0 += pre[j] * (cpre[pre.length-1-j-2] - (pre.length-1-(i-1)-1 >= 0 ? cpre[pre.length-1-(i-1)-1] : 0));
				//				s0 %= mod;
				// pre[j] * (i * suf[j+1+1] + (i-1) * suf[j+2+1] + ...)
				// pre[j] * (i * pre[P-1-(j+1+1)] + (i-1) * pre[P-1-(j+2+1)] + ...)
				// pre[j] * (wpre[P-1-(j+1+1)+1] * (ind-1)
				{
					int ind = pre.length-1-(j+2)+1;
					if(ind >= 0){
						s += dp[j] * (wpre[ind] + cpre[ind] * (i-(ind-1)) % mod) % mod;
					}
				}
				{
					int ind = pre.length-1-(j+(i+1)+1)+1;
					int oind = pre.length-1-(j+2)+1;
					if (ind >= 0) {
						s -= dp[j] * (wpre[ind] + cpre[ind] * (i-(oind-1)) % mod) % mod;
					}
				}
			}
			//			tr(i, s);
			//			s0 = s0 * i % mod;
//			S += System.nanoTime();
			ans = ans * (i+1) + s;
			ans %= mod;

			if(i == n-1)break;
			i++;
			for(int j = dp.length-i-1;j >= 0;j--){
				dp[j+i] -= dp[j];
				if(dp[j+i] < 0)dp[j+i] += mod;
			}
			for(int j = 1;j < dp.length;j++){
				dp[j] += dp[j-1];
				if(dp[j] >= mod)dp[j] -= mod;
			}
		}
		if(ans < 0)ans += mod;
		out.println(ans);

		//		int n = 5;
		//		int[] f = new int[n*(n-1)/2+1];
		//		for(int[] p : new IterablePermutation(n)){
		//			int inv = 0;
		//			for(int i = 0;i < n;i++){
		//				for(int j = i+1;j < n;j++){
		//					if(p[i] > p[j])inv++;
		//				}
		//			}
		//			f[inv]++;
		//		}
		//		tr(f);
		//		for(int T = ni();T > 0;T--)go();
	}

	void go()
	{

	}

	public static class IterablePermutation implements Iterable<int[]>, Iterator<int[]>
	{
		int[] a;
		boolean first = true;

		public IterablePermutation(int n) {
			assert n >= 1;
			a = new int[n];
			for(int i = 0;i < n;i++)a[i] = i;
		}

		public IterablePermutation(int... a) {
			this.a = Arrays.copyOf(a, a.length);
		}

		@Override
		public boolean hasNext() {
			if(first)return true;
			int n = a.length;
			int i;
			for(i = n - 2;i >= 0 && a[i] >= a[i+1];i--);
			return i != -1;
		}

		@Override
		public int[] next() {
			if(first) {
				first = false;
				return a;
			}
			int n = a.length;
			int i;
			for(i = n - 2;i >= 0 && a[i] >= a[i+1];i--);
			assert i != -1;
			int j;
			for(j = i + 1;j < n && a[i] < a[j];j++);
			int d = a[i]; a[i] = a[j - 1]; a[j - 1] = d;
			for(int p = i + 1, q = n - 1;p < q;p++,q--){
				d = a[p]; a[p] = a[q]; a[q] = d;
			}
			return a;
		}

		@Override
		public Iterator<int[]> iterator() {
			return this;
		}
	}

	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);

		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}

	public static void main(String[] args) throws Exception { new E1().run(); }

	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private 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 boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }

	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private 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);
	}

	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}

	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}

	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}

	private int ni() { return (int)nl(); }

	private 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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}