Problem: After the war, the supersonic rocket became the most common public transportation.

Each supersonic rocket consists of two "engines". Each engine is a set of "power sources". The first engine has n power sources, and the second one has m power sources. A power source can be described as a point (x_i, y_i) on a 2-D plane. All points in each engine are different.

You can manipulate each engine separately. There are two operations that you can do with each engine. You can do each operation as many times as you want.

  1. For every power source as a whole in that engine: (x_i, y_i) becomes (x_i+a, y_i+b), a and b can be any real numbers. In other words, all power sources will be shifted.
  2. For every power source as a whole in that engine: (x_i, y_i) becomes (x_i cos θ - y_i sin θ, x_i sin θ + y_i cos θ), θ can be any real number. In other words, all power sources will be rotated.



The engines work as follows: after the two engines are powered, their power sources are being combined (here power sources of different engines may coincide). If two power sources A(x_a, y_a) and B(x_b, y_b) exist, then for all real number k that 0 < k < 1, a new power source will be created C_k(kx_a+(1-k)x_b,ky_a+(1-k)y_b). Then, this procedure will be repeated again with all new and old power sources. After that, the "power field" from all power sources will be generated (can be considered as an infinite set of all power sources occurred).

A supersonic rocket is "safe" if and only if after you manipulate the engines, destroying any power source and then power the engine, the power field generated won't be changed (comparing to the situation where no power source erased). Two power fields are considered the same if and only if any power source in one field belongs to the other one as well.

Given a supersonic rocket, check whether it is safe or not.

Input

The first line contains two integers n, m (3 ≤ n, m ≤ 10^5) — the number of power sources in each engine.

Each of the next n lines contains two integers x_i and y_i (0≤ x_i, y_i≤ 10^8) — the coordinates of the i-th power source in the first engine.

Each of the next m lines contains two integers x_i and y_i (0≤ x_i, y_i≤ 10^8) — the coordinates of the i-th power source in the second engine.

It is guaranteed that there are no two or more power sources that are located in the same point in each engine.

Output

Print "YES" if the supersonic rocket is safe, otherwise "NO".

You can print each letter in an arbitrary case (upper or lower).

Examples

Input

3 4
0 0
0 2
2 0
0 2
2 2
2 0
1 1


Output

YES


Input

3 4
0 0
0 2
2 0
0 2
2 2
2 0
0 0


Output

NO

Note

The first sample:

<image> Those near pairs of blue and orange points actually coincide.

First, manipulate the first engine: use the second operation with θ = π (to rotate all power sources 180 degrees).

The power sources in the first engine become (0, 0), (0, -2), and (-2, 0).

<image>

Second, manipulate the second engine: use the first operation with a = b = -2.

The power sources in the second engine become (-2, 0), (0, 0), (0, -2), and (-1, -1).

<image>

You can examine that destroying any point, the power field formed by the two engines are always the solid triangle (0, 0), (-2, 0), (0, -2).

In the second sample, no matter how you manipulate the engines, there always exists a power source in the second engine that power field will shrink if you destroy it. 

Solution (in JAVA):

Solution:
import java.io.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Collections;

public class E {

	static int A,B;
	static ArrayList<Vector> hull1;
	static ArrayList<Vector> hull2;
	static long dist1[];
	static long dist2[];
	static int N;
	public static void main(String[] args) {
		JS in = new JS();
		A = in.nextInt();
		B = in.nextInt();
		ArrayList<Vector> p1s = new ArrayList<Vector>();
		ArrayList<Vector> p2s = new ArrayList<Vector>();
		for(int i = 0; i < A; i++) p1s.add(new Vector(in.nextLong(), in.nextLong()));
		for(int i = 0; i < B; i++) p2s.add(new Vector(in.nextLong(), in.nextLong()));
		
		hull1 = getHull(p1s);
		hull2 = getHull(p2s);
		
		if(hull1.size() != hull2.size()) {
			System.out.println("NO");
			return;
		}
		
		N = hull1.size();
		dist1 = new long[N];
		dist2 = new long[N];
		for(int i = 0; i < N; i++) {
			Vector p1 = hull1.get(i);
			Vector p2 = hull1.get((i+1)%N);
			dist1[i] = (p2.x-p1.x)*(p2.x-p1.x) + (p2.y-p1.y)*(p2.y-p1.y);
		}
		for(int i = 0; i < N; i++) {
			Vector p1 = hull2.get(i);
			Vector p2 = hull2.get((i+1)%N);
			dist2[i] = (p2.x-p1.x)*(p2.x-p1.x) + (p2.y-p1.y)*(p2.y-p1.y);
		}
		
		long dist2Double[] = new long[2*N];
		for(int i = 0; i < N; i++) {
			dist2Double[i] = dist2[i];
			dist2Double[N+i] = dist2[i];
		}
		
		//Run KMP on the distances
		ArrayList<Integer> distLocs = search(dist2Double, dist1, KMP_Construct(dist1));
		
		//Now run KMP on the angles and if there are matches on both, then the answer is yes
		long ang1[] = new long[N];
		long ang2[] = new long[N];
		for(int i = 0; i < N; i++) {
			Vector p2 = hull1.get(i);
			Vector p1 = hull1.get((i+N-1)%N);
			Vector p3 = hull1.get((i+1)%N);
			Vector v1 = new Vector(p3.x-p2.x, p3.y-p2.y);
			Vector v2 = new Vector(p1.x-p2.x, p1.y-p2.y);
			ang1[i] = v1.crs(v2);
		}
		for(int i = 0; i < N; i++) {
			Vector p2 = hull2.get(i);
			Vector p1 = hull2.get((i+N-1)%N);
			Vector p3 = hull2.get((i+1)%N);
			Vector v1 = new Vector(p3.x-p2.x, p3.y-p2.y);
			Vector v2 = new Vector(p1.x-p2.x, p1.y-p2.y);
			ang2[i] = v1.crs(v2);
		}
		long ang2Double[] = new long[2*N];
		for(int i = 0; i < N; i++) {
			ang2Double[i] = ang2[i];
			ang2Double[N+i] = ang2[i];
		}
		ArrayList<Integer> angLocs = search(ang2Double, ang1, KMP_Construct(ang1));
		
		long dot1[] = new long[N];
		long dot2[] = new long[N];
		long dot2Double[] = new long[2*N];
		for(int i = 0; i < N; i++) {
			Vector p2 = hull1.get(i);
			Vector p1 = hull1.get((i+N-1)%N);
			Vector p3 = hull1.get((i+1)%N);
			dot1[i] = (p1.sub(p2)).dot(p3.sub(p2));
		}
		for(int i = 0; i < N; i++) {
			Vector p2 = hull2.get(i);
			Vector p1 = hull2.get((i+N-1)%N);
			Vector p3 = hull2.get((i+1)%N);
			dot2[i] = (p1.sub(p2)).dot(p3.sub(p2));
		}
		for(int i = 0; i < N; i++) {
			dot2Double[i]=dot2[i];
			dot2Double[N+i]=dot2[i];
		}
		ArrayList<Integer> dotLocs = search(dot2Double, dot1, KMP_Construct(dot1));
		boolean b1[][] = new boolean[3][3*N];
		for(Integer ii : distLocs) b1[0][ii]=true;
		for(Integer ii : angLocs) b1[1][ii]=true;
		for(Integer ii : dotLocs) b1[2][ii]=true;
		boolean good = false;
		for(int i = 0; i < 3*N; i++) {
			if(b1[0][i]&&b1[1][i]&&b1[2][i])good=true;
		}
		if(good) {
			System.out.println("YES");
		}
		else {
			System.out.println("NO");
		}
		
	}

	static boolean eq(double a, double b) {
		return Math.abs(a-b) < 1e-6;
	}
	
	// Given a pattern string w, return the prefix array. //%
	// p[i] indicates the length of the longest prefix //%
	// that is also a substring ending at i.  O(|w|) //%
	static int[] KMP_Construct(long[] w) {
		int n = w.length + 1, k = 0;  int[] p = new int[n];  p[1] = 0;
		for(int i = 2; i < n; ++i) {
			while(k > 0 && w[k] != w[i-1]) k = p[k];
			if(w[k] == w[i-1]) k++;
			p[i] = k;
		}
		return p;
	}

	// Given the prefix array of a pattern, search the //%
	// text for all occurrences of the pattern.  O(|s|) //%
	static ArrayList<Integer> search(long[] s, long[] w, int[] p) {
		int k = 0;  ArrayList<Integer> locs = new ArrayList<>();
		for(int i = 0; i < s.length; ++i) {
			while(k > 0 && w[k] != s[i]) k = p[k];
			if(w[k] == s[i]) k++;
			if(k == w.length) { locs.add(i-w.length+1);  k = p[k]; }
		}
		return locs;
	}
	
	// Returns the convex hull in COUNTER-CLOCKWISE order.  Vector: Compare X then Y.
	public static ArrayList<Vector> getHull(ArrayList<Vector> ps) {
	    ArrayList<Vector> s = (ArrayList<Vector>) ps.clone();
	    Collections.sort(s);
	    
	    int n = s.size(), j = 2, k = 2;

	    Vector[] lo = new Vector[n], up = new Vector[n];
	    lo[0] = s.get(0);  lo[1] = s.get(1);
	                
	    for (int i = 2; i < n; i++) {
	        Vector p = s.get(i);
	        while (j > 1 && !RT(lo[j - 2], lo[j - 1], p))  j--;
	        lo[j++] = p;
	    }
	                
	    up[0] = s.get(n - 1);  up[1] = s.get(n - 2);

	    for (int i = n - 3; i >= 0; i--) { // note difference
	        Vector p = s.get(i);
	        while (k > 1 && !RT(up[k - 2], up[k - 1], p))  k--;
	        up[k++] = p;
	    }
	                
	    ArrayList<Vector> res = new ArrayList<Vector>();
	    for (int i = 0; i < k; i++) res.add(up[i]);
	    for (int i = 1; i < j - 1; i++) res.add(lo[i]);

	    // Only needed if want the two halves of the polygon
	    Vector[] hullUp = new Vector[k];
	    for(int i = 0; i < k; i++) hullUp[i] = up[k - i - 1];
	    Vector[] hullLo = new Vector[j];
	    for(int i = 0; i < j; i++) hullLo[i] = lo[i];

	    return res;
	}
	static boolean RT(Vector a, Vector b, Vector c) { return b.sub(a).cross(c.sub(a)).z > 0; }
	
	static class Vector implements Comparable<Vector> {
	    public long x, y, z; //%
	    public long x0 = 0, y0 = 0, z0 = 0; //%
	    public static double epsilon = 1e-6; //%
	    public static Vector ORIGIN = new Vector(0, 0, 0); //%
	    public static int curId = 0; //%
	    public int id = Vector.curId++; //%

	    //#
	    // Constructor for normal vector
	    public Vector(long xx, long yy, long zz) {
	        x = xx;
	        y = yy;
	        z = zz;
	    }

	    // Constructor for 2d normal vector
	    public Vector(long xx, long yy) {
	        x = xx;
	        y = yy;
	        z = 0;
	    }

	    // Constructor for ray/line vector
	    public Vector(Vector a, Vector b) {
	        x = b.x - (x0 = a.x);
	        y = b.y - (y0 = a.y);
	        z = b.z - (z0 = a.z);
	    }

	    //$
	    
	    //#
	    public static boolean equals(double a, double b) {
	        return Math.abs(a - b) < epsilon;
	    }

	    public Vector add(Vector v) {
	        return new Vector(x + v.x, y + v.y, z + v.z);
	    }

	    public Vector sub(Vector v) {
	        return new Vector(x - v.x, y - v.y, z - v.z);
	    }
	    

	    public double mag() {
	        return Math.sqrt((x*x) + (y*y) + (z*z));
	    }
	    
	    public double mag2() {
	        return dot(this);
	    }

	    public long dot(Vector v) {
	        return (x * v.x) + (y * v.y) + (z * v.z);
	    }
	    
	    public long crs(Vector v) {
	    	return this.cross(v).z;
	    }
	    public Vector cross(Vector v) { return new Vector(y*v.z - z*v.y, z*v.x - x*v.z, x*v.y - y*v.x); }
	    
	    // Returns this vector rotated 90 degrees clockwise //%
	    public Vector orthoCW() { return new Vector(y, -x, z); }

	    // Returns this vector rotated 90 degrees counter-clockwise //%
	    public Vector orthoCCW() { return new Vector(-y, x, z); }


	    //#
	    public boolean pointOnLine(Vector p) {
	        if(equals(x, 0.0)) return equals(p.x, x0);
	        return equals(p.y - y0, (y/x) * (p.x - x0));
	    }

	    //#
	    public int compareTo(Vector p) {
	        if (y == p.y) return Double.compare(x, p.x);
	        return Double.compare(y, p.y);
	    }
	    //$
	    
	    //#
	    // Compares a and b with whichever comes first in a positive circular sweep
	    // Works best for longs
	    public static int compare(Vector a, Vector b) {
	        int res = 0;

	        if (a.x < 0) res += a.y >= 0 ? 1 : 2;
	        else if (a.y < 0) res += 3;
	        
	        if (b.x < 0) res -= b.y >= 0 ? 1 : 2;
	        else if (b.y < 0) res -= 3;

	        if(res == 0) {
	            Vector cross = a.cross(b);  if(cross.z == 0) return 0;
	            if(cross.z > 0) return -1;  else  return 1;
	        }

	        return res;
	    }
	    //$
	    
	    //#
	    public String toString() {
	        if(equals(x0, 0.0) && equals(y0, 0.0) && equals(z0, 0.0))
	            return String.format("<%.2f, %.2f, %.2f>", x, y, z);
	        return String.format("<%.2f + %.2ft, %.2f + %.2ft, %.2f + %.2ft>", x0, x, y0, y, z0, z);
	    } //$
	}
	
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;
		
		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}
		
		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}
		
		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}
		
		public int nextInt() {
			return (int)nextLong();
		}
		
		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}
		
		public double nextDouble() {
		    while(c!='.'&&c!='-'&&(c <'0' || c>'9')) c = nextChar();
		    boolean neg = c=='-';
		    if(neg)c=nextChar();
		    boolean fl = c=='.';
		    double cur = nextLong();
		    if(fl) return neg ? -cur/num : cur/num;
		    if(c == '.') {
			double next = nextLong();
			return neg ? -cur-next/num : cur+next/num;
		    }
		    else return neg ? -cur : cur;
		}
		
		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}
		
		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
	
}