Problem: Recall that the bracket sequence is considered regular if it is possible to insert symbols '+' and '1' into it so that the result is a correct arithmetic expression. For example, a sequence "(()())" is regular, because we can get correct arithmetic expression insering symbols '+' and '1': "((1+1)+(1+1))". Also the following sequences are regular: "()()()", "(())" and "()". The following sequences are not regular bracket sequences: ")(", "(()" and "())(()".

In this problem you are given two integers n and k. Your task is to construct a regular bracket sequence consisting of round brackets with length 2·n with total sum of nesting of all opening brackets equals to exactly k. The nesting of a single opening bracket equals to the number of pairs of brackets in which current opening bracket is embedded.

For example, in the sequence "()(())" the nesting of first opening bracket equals to 0, the nesting of the second opening bracket equals to 0 and the nesting of the third opening bracket equal to 1. So the total sum of nestings equals to 1.

Input

The first line contains two integers n and k (1 ≤ n ≤ 3·105, 0 ≤ k ≤ 1018) — the number of opening brackets and needed total nesting.

Output

Print the required regular bracket sequence consisting of round brackets.

If there is no solution print "Impossible" (without quotes).

Examples

Input

3 1


Output

()(())

Input

4 6


Output

(((())))

Input

2 5


Output

Impossible

Note

The first example is examined in the statement.

In the second example the answer is "(((())))". The nesting of the first opening bracket is 0, the nesting of the second is 1, the nesting of the third is 2, the nesting of fourth is 3. So the total sum of nestings equals to 0 + 1 + 2 + 3 = 6.

In the third it is impossible to construct a regular bracket sequence, because the maximum possible total sum of nestings for two opening brackets equals to 1. This total sum of nestings is obtained for the sequence "(())".

Solution (in JAVA):

Solution:
	import java.io.*;



import java.math.*;
import java.nio.file.attribute.AclEntry.Builder;
import java.security.KeyStore.Entry;
import java.util.*;


	 
	public  class Khatri {
		private InputStream is;
		private PrintWriter out;
		int time = 0, DP[], start[], end[], dist[],  black[];
		static int MOD = (int)(1e9+7);
		int arr[];
		int weight[][];
		int x[];
		int y[];
		int parent[];
		int MAX = 800000, N, K, L;
		long red[];
		ArrayList<Integer>[] amp;
		HashSet<Integer> hs = new HashSet<>();
		long Dp[][][][] = new long[110][110][12][12];
		public static void main(String[] args) throws Exception 
		{
			new Thread(null, new Runnable() 
			{
			public void run() 
			{
				try {
	 
			//new CODEFORCES().soln();
			} catch (Exception e) 
				{
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
			new Khatri().soln();
		}
		char ch[][];
		//int ans = 0, cnt = 0, Q;
		int n1, n2, k1, k2, M;
		static ArrayList<Integer>[] g;
        static ArrayList<Integer> ar[];
		static long ok[];	
		//static int a[];
		static int phi[]=new int[500005];
		void solve()
        {
			long n=nl();
			long k=nl();
			if(k>(((n)*(n-1))/2))
	{
		out.print("Impossible");
		return;
	}
			long low=1;
			long high=(long)1e9;
			long ans=-1;
			long finn=0;
			long fink=0;
			while(low<=high)
			{
				long mid=(low+high)/2;
			    long temp=(mid*(mid-1));temp/=2;
			    if(temp<=k)
			    {
			    	long rem=k-temp;
			    	long remn=n-mid;
			    	if(remn*mid>=rem)
			    	{
			    		ans=mid;
			    		fink=rem;
			    		finn=remn;
			    		break;
			    	}
			    	else
			    	{
			    	low=mid+1;	
			    	}
			    }
			    else
			    {
			    	high=mid-1;
			    }
			    
			}
			StringBuilder ans1=new StringBuilder();
			for(int i=1;i<=ans;i++)
			{
				ans1.append('(');
			}
			for(int i=1;i<=ans;i++)
                ans1.append(')');
			long an[]=new long[(int)ans1.length()+1];
			//System.out.println(fink+" "+finn+" "+ans);
			for(long i=ans;i>=1;i--)
			{
				long tempr=fink/i;
				an[(int)i]=tempr;
				fink-=(tempr*i);
				finn-=(tempr);
				if(fink==0||finn==0)
					break;
			}
			StringBuilder sb=new StringBuilder();
			for(int i=0;i<ans1.length();i++)
			{
				sb.append(ans1.charAt(i));
				if(an[i+1]>0)
				{
					for(int j=1;j<=an[i+1];j++){
					sb.append("()");
					
					}
				}
				
				
			}
			
			if(finn>0&&fink==0)
			{
				for(int i=1;i<=finn;i++)
					sb.append("()");
			}
			System.out.println(sb);
			
			
		    
        } 
	
		
			
        
		
		
	    
		
              
       

       
       
            boolean isPrime(int x)
            {
            if(x==0||x==1)
            	return false;
			for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
			return true;
		}
	    int  p ;
		void buildGraph(int n)
		{
			for(int i = 0; i<n ;i++){
				int x1 = ni() -1, y1 = ni()-1;
				amp[x1].add(y1);
				amp[y1].add(x1);
				x[i] = x1; y[i] = y1;
			}
		}
		long get(int x){
			long val = 0;
			for(int i = 0; i< N; i++){
				val += Math.abs(x-arr[i]);
				x+=L;
			}
			return val;
		}
		
		long modInverse(long a, long mOD2){
	        return  power(a, mOD2-2, mOD2);
		}
		long power(long x, long y, long m)
		{
			if (y == 0)
	    return 1;
		long p = power(x, y/2, m) % m;
		p = (p * p) % m;
	 
		return (y%2 == 0)? p : (x * p) % m;
		}
		
		public static long gcd(long a, long b){
			if(b==0) return a;
			return gcd(b,a%b);
		}
		
		public static int[] shuffle(int[] a, Random gen){
			for(int i = 0, n = a.length;i < n;i++)
			{ 
				int ind = gen.nextInt(n-i)+i; 
				int d = a[i]; 
				a[i] = a[ind];
				a[ind] = d; 
			} 
		return a; 
		}
	 
		
		class Pair1 implements Comparable<Pair1>{
			String s;
			int val;
			Pair1(String s,int time){
			this.s=s;
			this.val=time;
			}
			public int hashCode() {
				return Objects.hash();
			}
			
			@Override
			public int compareTo(Pair1 arg0) {
				return (int)(arg0.val-val);
			}
			
		}
		long power(long x, long y, int mod){
			long ans = 1;
			while(y>0){
				if(y%2==0){
					x = (x*x)%mod;
					y/=2;
				}
				else{
					ans = (x*ans)%mod;
					y--;
				}
			}
			return ans;
		}
		void soln() {
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
			//out.close();
			out.flush();
			//tr(System.currentTimeMillis() - s + "ms");
		}
	 
	 
		// To Get Input
		// Some Buffer Methods
		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[][] nm(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++)
			{
				for(int j=0;j<m;j++)
					map[i][j]=ni();
			}
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private 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 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();
			}
		}
	 
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	 
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}