A. Petya and Inequiations
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Little Petya loves inequations. Help him find n positive integers a 1, a 2, ..., a n, such that the following two conditions are satisfied:

  • a 1 2 + a 2 2 + ... + a n 2 ≥ x
  • a 1 + a 2 + ... + a n ≤ 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