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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int v[200002];
long long int max(long long int a, long long int b) {
  if (a > b) return a;
  return b;
}
long long int find(long long int x) {
  if (x == v[x]) return x;
  return v[x] = find(v[x]);
}
bool merge(long long int x, long long int y) {
  long long int a = find(x);
  long long int b = find(y);
  if (a != b) {
    v[a] = b;
    return true;
  }
  return false;
}
void build(vector<long long int> &tree, long long int i, long long int l,
           long long int r, vector<long long int> &v) {
  if (l == r) {
    tree[i] = v[l];
    return;
  }
  long long int mid = (l + r) / 2;
  build(tree, 2 * i, l, mid, v);
  build(tree, 2 * i + 1, mid + 1, r, v);
  tree[i] = tree[2 * i] + tree[2 * i + 1];
}
long long int get(vector<long long int> &tree, long long int i, long long int l,
                  long long int r, long long int ql, long long int qr,
                  vector<long long int> &lazy) {
  if (lazy[i] != -1) {
    if (lazy[i] == 0) {
      tree[i] = 0;
      if (l != r) {
        lazy[2 * i] = 0;
        lazy[2 * i + 1] = 0;
      }
    } else {
      tree[i] = lazy[i];
      long long int mid = (l + r) / 2;
      if (l != r) {
        lazy[2 * i] = mid - l + 1;
        lazy[2 * i + 1] = r - mid;
      }
    }
    lazy[i] = -1;
  }
  if (ql > r || qr < l) return 0;
  if (ql <= l && r <= qr) return (tree[i]);
  long long int mid = (l + r) / 2;
  return (get(tree, 2 * i, l, mid, ql, qr, lazy) +
          get(tree, 2 * i + 1, mid + 1, r, ql, qr, lazy));
}
void update(vector<long long int> &tree, long long int i, long long int l,
            long long int r, long long int ql, long long int qr,
            long long int val, vector<long long int> &lazy) {
  long long int mid = (l + r) / 2;
  if (ql > r || qr < l)
    return;
  else if (ql <= l && r <= qr) {
    tree[i] = (val == 0) ? 0 : r - l + 1;
    if (l != r) {
      lazy[2 * i] = (val == 0) ? 0 : mid - l + 1;
      lazy[2 * i + 1] = (val == 0) ? 0 : r - mid;
    }
    lazy[i] = -1;
  } else {
    update(tree, 2 * i, l, mid, ql, qr, val, lazy);
    update(tree, 2 * i + 1, mid + 1, r, ql, qr, val, lazy);
    tree[i] = tree[2 * i] + tree[2 * i + 1];
  }
}
long long int make(vector<vector<long long int> > &v, long long int a,
                   long long int b, long long int ini, long long int pre,
                   long long int use) {
  if ((ini + a) % 10 == pre || (ini + b) % 10 == pre) {
    v[ini][pre] = 1;
    return 1;
  }
  if (use > 10) return 10000000000001;
  if (v[ini][pre] != 0) {
    return v[ini][pre];
  } else {
    v[ini][pre] = min(make(v, a, b, (ini + a) % 10, pre, use + 1),
                      make(v, a, b, (ini + b) % 10, pre, use + 1)) +
                  1;
    return v[ini][pre];
  }
}
bool check(vector<long long int> &v, int x, long long int n) {
  long long int p = 0;
  long long int a = 0;
  if (x == 0) return false;
  while (p < n && a < n) {
    while (a < n && v[a] != 1) {
      a++;
    }
    while (p < n && v[p] != 2) {
      p++;
    }
    if (a == n) {
      return true;
    }
    if (p == n) {
      return false;
    }
    if (a > p) {
      a = max(p + x + 1, a);
    } else {
      long long int d = p - a;
      long long int l = max((x - 2 * d), (x - d < 0) ? -1 : (x - d) / 2);
      if (l < 0) {
        return false;
      }
      a = p + l + 1;
    }
    p++;
  }
  if (a < n) {
    return false;
  }
  return true;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long int te = 1;
  while (te--) {
    long long int n, k;
    cin >> n >> k;
    long long int count = 0;
    long long int odd = 0;
    long long int eve = 0;
    string st = "";
    for (long long int i = 0; i < 2 * n; i++) {
      if (count <= k) {
        st += "(";
        k -= count;
        count++;
        odd++;
      } else if (count > k) {
        st += ')';
        count--;
        eve++;
      }
    }
    long long int co = 0;
    for (long long int i = 0; i < 2 * n; i++) {
      if (st[i] == '(')
        co++;
      else {
        co--;
      }
      if (co < 0) {
        cout << "Impossible" << endl;
        break;
      }
    }
    if (co > 0) {
      cout << "Impossible" << endl;
      break;
    }
    cout << st << endl;
  }
  return 0;
}