Problem Statement

For an integer N greater than or equal to 2, there are $\frac{N(N - 1)}{2}$ pairs of integers (x, y) such that $1 \leq x \lt y \leq N$.
Consider the sequence of these pairs sorted in the increasing lexicographical order. Let $(x_1, y_1), \dots, (x_{R - L + 1}, y_{R - L + 1})$ be its $L-th, (L+1)-th, \ldots$, and $R-th elements, respectively. On a sequence A = (1, \dots, N)$, We will perform the following operation for $i = 1, \dots, R-L+1$ in this order:

• Swap A_{x_i} and A_{y_i}.

Find the final A after all the operations.
We say that (a, b) is smaller than (c, d) in the lexicographical order if and only if one of the following holds:

• $a \lt c$
• a = c and $b \lt d$

Input

Input is given from Standard Input in the following format:
N L R

Output

Print the terms of A after all the operations in one line, separated by spaces.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq L \leq R \leq \frac{N(N-1)}{2}$
• All values in input are integers.

Sample Input 1

5 3 6

Sample Output 1

5 1 2 3 4

Consider the sequence of pairs of integers such that $1 \leq x \lt y \leq N$ sorted in the increasing lexicographical order. Its 3-rd, 4-th, 5-th, and 6-th elements are (1, 4), (1, 5), (2, 3), (2, 4), respectively.
Corresponding to these pairs, A transitions as follows.
$(1, 2, 3, 4, 5) \rightarrow (4, 2, 3, 1, 5) \rightarrow (5, 2, 3, 1, 4) \rightarrow (5, 3, 2, 1, 4) \rightarrow (5, 1, 2, 3, 4)$

Sample Input 2

10 12 36

Sample Output 2

1 10 9 8 7 4 3 2 5 6

见题面 Input 部分

见题面 Output 部分