Little Petya loves inequations. Help him find n positive integers a₁, a₂, ..., a_n, such that the following two conditions are satisfied:

a₁² + a₂² + ... + a_n² ≥ x
a₁ + a₂ + ... + 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.

Petya and Inequiations

Examples