Solve the programming task below in a Python markdown code block.
Little Petya loves inequations. Help him find n positive integers a1, a2, ..., an, such that the following two conditions are satisfied:

  * a12 + a22 + ... + an2 ≥ x
  * a1 + a2 + ... + an ≤ y

Input

The first line contains three space-separated integers n, x and y (1 ≤ n ≤ 105, 1 ≤ x ≤ 1012, 1 ≤ y ≤ 106).

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is recommended to use cin, cout streams or the %I64d specificator.

Output

Print n positive integers that satisfy the conditions, one integer per line. If such numbers do not exist, print a single number "-1". If there are several solutions, print any of them.

Examples

Input

5 15 15


Output

4
4
1
1
2


Input

2 3 2


Output

-1


Input

1 99 11


Output

11