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.*;

/**
 * 18-Sep-2017
 * 11:30:05 PM
 * @author HulkBuster
 * 
 */
public class CF847C {
public static int mod = (int) (1e9 + 7);
public static InputReader in;
public static PrintWriter out;

public static void solve() throws FileNotFoundException {

	in = new InputReader(System.in);
	out = new PrintWriter(System.out);
	long n = in.ni();
	long k = in.nl();
	
	long max = (n*(n-1))/2;	
	
	if(max < k)
		out.println("Impossible");
	else{
		long start = 0;
		long end = (long)Math.sqrt(2*k);
		
		long ans =-1;
		while(start<=end){
			long mid = (start+end)/2;
			if(mid*(mid+1)<=2*k){
				ans =mid;
				start = mid+1;
			}
			else{
				end = mid-1;
			}
			
		}
		long z = ans;
		if(z==0){
			while(n-->0)
				out.print("()");
		}
		else{
			//out.println(z+1);
			z = z+1;
			k = k - (z*(z-1))/2;
			for(int i=1;i<=z;i++)
				out.print("(");
			for(int i = (int)z;i>k;i--)
				out.print(")");
			if(k>0)out.print("()");
			for(int i = (int)(k);i>=1;i--)
				out.print(")");
			n = n - z;
			if(k>0)
				n--;
			while(n-->0)
				out.print("()");
			
		}
		//out.println(z);
		
		
		
		//out.println("n"+n);
		
	}
	out.close();
}

public static void main(String[] args) {
	new Thread(null, new Runnable() {
		public void run() {
			try {
				solve();
			} catch (Exception e) {
				e.printStackTrace();
			}
		}
	}, "1", 1 << 26).start();
}

static class Pair implements Comparable<Pair> {

	int x, y, i;

	Pair(int x, int y, int i) {
		this.x = x;
		this.y = y;
		this.i = i;
	}

	Pair(int x, int y) {
		this.x = x;
		this.y = y;
	}

	public int compareTo(Pair o) {
		if (this.x != o.x)
			return Integer.compare(this.x, o.x);
		else
			return Integer.compare(this.y, o.y);
		//return 0;
	}

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

	public int hashCode() {
		return new Integer(x).hashCode() * 31 + new Integer(y).hashCode() + new Integer(i).hashCode() * 37;
	}

}

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

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

public static long mul(long a, long b) {
	long x = (a * b);
	while (x >= mod)
		x -= mod;
	return x;
}

public 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;
}

public static String rev(String s) {
	StringBuilder sb = new StringBuilder(s);
	sb.reverse();
	return sb.toString();
}

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

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

public 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;
}

public 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;
}

public 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);
}

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

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

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

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

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

public static long pow(long n, long p) {
	long result = 1;
	if (p == 0)
		return 1;
	if (p == 1)
		return n;
	while (p != 0) {
		if (p % 2 == 1)
			result *= n;
		p >>= 1;
		n *= n;
	}
	return result;
}

public 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 ni() {
		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 nl() {
		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[] nIArr(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = ni();
		}
		return a;
	}

	public long[] nLArr(int n) {
		long a[] = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = nl();
		}
		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);
	}

}
}