Problem Statement

For a sequence of integers $P = (P_1, \ldots, P_M)$, let f(P) denote the sequence obtained by inserting P_i + P_{i+1} between P_i and P_{i+1} for each $1\leq i\leq M-1$.
More formally:

• Let Q_i = P_i + P_{i+1} for each $1\leq i\leq M - 1$.
• Let f(P) be defined as a sequence of $2M-1 integers f(P) = (P_1, Q_1, P_2, Q_2, \ldots, P_{M-1}, Q_{M-1}, P_M)$.

Given are three positive integers a, b, and N where $a, b\leq N$. Let us begin with a sequence A = (a, b) and define $a sequence B = (B_1, B_2, \ldots)$ as follows.

• Do the following N times: replace A with f(A).
• Then, remove from A all values greater than N and let B be the resulting sequence.

Find $B_L, \ldots, B_R$.

Input

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

Output

Print $a line containing B_L, \ldots, B_R$, with a space in between.

Constraints

• $1\leq N\leq 3\times 10^5$
• $1\leq a, b\leq N$
• $1\leq L\leq R\leq 10^{18}$
• $R - L < 3\times 10^5$
• R is at most the number of elements in the sequence B.

Sample Input 1

1 1 4
1 7

Sample Output 1

1 4 3 2 3 4 1

Initially, A = (1, 1). The replacements of A with f(A) take place as follows.

• After the first replacement: A = (1, 2, 1).
• After the second replacement: A = (1, 3, 2, 3, 1).
• After the third replacement: A = (1, 4, 3, 5, 2, 5, 3, 4, 1).
• After the fourth replacement: A = (1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1).

Thus, we have B = (1, 4, 3, 2, 3, 4, 1). We should report the 1-st through 7-th elements of this sequence.

Sample Input 2

1 1 4
2 5

Sample Output 2

4 3 2 3

Again, we have B = (1, 4, 3, 2, 3, 4, 1). We should report the 2-nd through 5-th elements of this sequence.

Sample Input 3

2 1 10
5 15

Sample Output 3

8 3 10 7 4 9 5 6 7 8 9

Sample Input 4

10 10 10
2 2

Sample Output 4

10

见题面 Input 部分

见题面 Output 部分