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.util.*;
import java.io.*;
import java.math.BigInteger;

/**
 *
 * @author usquare
 * 
 */

public class ProblemD
{

    static long mod = (int) (1e9+7);
    static InputReader in;
    static PrintWriter out;
    
    static void solve()
    {

        in = new InputReader(System.in);
        out = new PrintWriter(System.out);  
        
        long n = in.nextLong();
        long k = in.nextLong();
        
        if((n * (n - 1)) / 2 < k) out.println("Impossible");
        else{
            StringBuilder str = new StringBuilder();

            long j = 1;
            long cnt = 0;
            while(cnt <= k){
                j++;
                cnt = (j * (j - 1)) / 2;
            }
            j--;
            k -= (j * (j - 1)) / 2;
            for(int i = 1; i <= j; i++){
                str.append('(');
                if(i == k) str.append("()");
            }
            for(int i = 0; i < j; i++) str.append(')');
            
            if(str.toString().length() > 2 * n) out.println("Impossible");
            else{
                while(str.length() < 2 * n) str.append("()");
                out.println(str.toString());
            }
            
        }
        
        out.close();

    }
    
    
    public static void main(String[] args)
    {

        new Thread(null,new Runnable()
        {
            @Override
            public void run()
            {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();
    }

    static class Pair implements Comparable<Pair>
    {

        int i;
        long x, y;
        
	Pair (long x,long y,int i)
        {
		this.x = x;
		this.y = y;
                this.i = i;
	}
        
	public int compareTo(Pair o)
        {
                    return Long.compare(this.i,o.i);
	}

        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString()
        {
            return x + " "+ y + " "+i;
        }
        
        public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }
    
    } 


    static class Merge
    {

        public static void sort(int inputArr[])
        {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }

        private static void doMergeSort(int[] arr,int lowerIndex, int higherIndex)
        {        
            if (lowerIndex < higherIndex)
            {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }

        private static void mergeParts(int[]array,int lowerIndex, int middle, int higherIndex)
        {
            int[] temp=new int[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++)
            {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex)
            {
                if (temp[i-lowerIndex] < temp[j-lowerIndex])
                {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else
                {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle)
            {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex)
            {
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }

    }

    static long add(long a,long b)
    {
        long x = a + b;
        if(x >= mod) x -= mod;
        return x;
    }

    static long sub(long a,long b)
    {
        long x= a - b ;
        if(x < 0) x += mod;
        return x;
    }

    static long mul(long a,long b)
    {
        a %= mod;
        b %= mod;
        long x = a*b;
        return x%mod;
    }


    static boolean isPal(String s)
    {
        for(int i=0, j=s.length()-1;i<=j;i++,j--)
        {
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
    }
    static String rev(String s)
    {
                StringBuilder sb=new StringBuilder(s);
                sb.reverse();
                return sb.toString();
    }

    static long gcd(long x,long y)
    {
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y)
    {
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long gcdExtended(long a,long b,long[] x)
    {

        if(a==0)
        {
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);

        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];

        return gcd;
    }


    static long mulmod(long  a,long b,long m)
    {
        if (m <= 1000000009) return a * b % m;

        long res = 0;
        while (a > 0)
        {
            if ((a&1)!=0)
            {
                res += b;
                if (res >= m) res -= m;
            }
            a >>= 1;
            b <<= 1;
            if (b >= m) b -= m;
        }
        return res;
    }

    static int abs(int a,int b)
    {
        return (int)Math.abs(a-b);
    }

    public static long abs(long a,long b)
    {
        return (long)Math.abs(a-b);
    }

    static int max(int a,int b)
    {
        if(a>b)
                return a;
        else
                return b;
    }

    static int min(int a,int b)
    {
        if(a>b)
                return b;
        else 
                return a;
    }

    static long max(long a,long b)
    {
        if(a>b)
                return a;
        else
                return b;
    }

    static long min(long a,long b)
    {
        if(a>b)
                return b;
        else 
                return a;
    }

    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result>=m)
            result%=m;
            p >>=1;
            n*=n;
            if(n>=m)
            n%=m;
        }
        return result;
    }

    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

    static void debug(Object... o)
    {
            System.out.println(Arrays.deepToString(o));
    }

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
                this.stream = stream;
        }

        public int snext()
        {
                if (snumChars == -1)
                        throw new InputMismatchException();
                if (curChar >= snumChars)
                {
                        curChar = 0;
                        try
                        {
                                snumChars = stream.read(buf);
                        } catch (IOException e)
                        {
                                throw new InputMismatchException();
                        }
                        if (snumChars <= 0)
                                return -1;
                }
                return buf[curChar++];
        }

        public int nextInt()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                int res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public long nextLong()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                long res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public int[] nextIntArray(int n)
        {
                int a[] = new int[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextInt();
                }
                return a;
        }

        public long[] nextLongArray(int n)
        {
                long a[] = new long[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextLong();
                }
                return a;
        }

        public String readString()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }

        public String nextLine()
        {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
                if (filter != null)
                        return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
                return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
                public boolean isSpaceChar(int ch);
        }

    }
}