Petya and Inequiations

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

inputFormat

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.

outputFormat

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

样例

5 15 15

11
1
1
1
1

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