The Legend Was Invented, but Not the Name#11695

The Legend Was Invented, but Not the Name

1 second

256 megabytes

Very hard

How did the evil Chmyaaax become evil? The evil Chmyaaax was once a regular Max who was solving problems on Eolymp. He became evil because of a problem he couldn't solve. So, the legend about him was born, and although the truth about it remains unknown, the problem itself has survived. So, here is Frus' record about this problem:

You are given two numbers $x$ and $y$ . You need to find an array of numbers such that the sum of the squares of these numbers is equal to $1 0^{15} + x$ 10^{15} + x, and the sum of the cubes is equal to $1 0^{15} + y$ 10^{15} + y. Formally, you need to find any array of numbers such that:

a_{1}^{2} + a_{2}^{2} + \dots + a_{m}^{2} = 1 0^{15} + x

a_1^2 + a_2^2 + \dots + a_m^2 = 10^{15} + x

a_{1}^{3} + a_{2}^{3} + \dots + a_{m}^{3} = 1 0^{15} + y

a_1^3 + a_2^3 + \dots + a_m^3 = 10^{15} + y

where $m$ is the number of elements in this array.

Input

The first and only line contains two integers $x$ and $y$ ( $0 \leq x, y \leq 1 0^{9}$ 0 \le x, y \le 10^{9}).

Output

In the first line, you need to output only one integer $n$ ( $1 \leq n \leq 2 \cdot 1 0^{5}$ 1 \le n \le 2 \cdot 10^5) — the number of distinct elements in the array $a$ .

In the next $n$ lines, you need to output the information about the array in the following form:

$c_{i} k_{i}$ c_i\,k_i

That means that there are $k_{i}$ k_i elements in the array that are equal to $c_{i}$ c_i ( $1 \leq i \leq n$ 1 \le i \le n, $1 \leq c_{i} \leq 1 0^{9}$ 1 \le c_i \le 10^{9}, $1 \leq k_{i} \leq 1 0^{16}$ 1 \le k_i \le 10^{16}).

All $c_{i}$ c_i must be pairwise distinct.

If there are multiple answers, you can output any of them.

If there are no such arrays, you need to output $- 1$ .

Examples

Example

Example 1

Example 2

Note

In the first example, there are $1 0^{15} - 3$ 10^{15} - 3 elements equal to $1$ and $1$ element equal to $2$ . In this way, the sums are following:

$(1 0^{15} - 3) \cdot 1^{2} + 1 \cdot 2^{2} = 1 0^{15} + 1$ (10^{15} - 3) \cdot 1^2 + 1 \cdot 2^2 = 10^{15} + 1

$(1 0^{15} - 3) \cdot 1^{3} + 1 \cdot 2^{3} = 1 0^{15} + 5$ (10^{15} - 3) \cdot 1^3 + 1 \cdot 2^3 = 10^{15} + 5

In the second example, there are $1 0^{15} + 1$ 10^{15} + 1 elements equal to $1$ and $1$ entry of each number from $2$ to $5$ :

$(1 0^{15} + 1) \cdot 1^{2} + 1 \cdot 2^{2} + 1 \cdot 3^{2} + 1 \cdot 4^{2} + 1 \cdot 5^{2} = (1 0^{15} + 1) + 4 + 9 + 16 + 25 = 1 0^{15} + 55$ (10^{15} + 1) \cdot 1^2 + 1 \cdot 2^2 + 1 \cdot 3^2 + 1 \cdot 4^2 + 1 \cdot 5^2 = (10^{15} + 1) + 4 + 9 + 16 + 25 = 10^{15} + 55

$(1 0^{15} + 1) \cdot 1^{3} + 1 \cdot 2^{3} + 1 \cdot 3^{3} + 1 \cdot 4^{3} + 1 \cdot 5^{3} = (1 0^{15} + 1) + 8 + 27 + 64 + 125 = 1 0^{15} + 225$ (10^{15} + 1) \cdot 1^3 + 1 \cdot 2^3 + 1 \cdot 3^3 + 1 \cdot 4^3 + 1 \cdot 5^3 = (10^{15} + 1) + 8 + 27 + 64 + 125 = 10^{15} + 225

In the third sample, it can be shown that there are no arrays that would satisfy the conditions.

Scoring

( $12$ points): $x = y$ x = y;
( $13$ points): $x > y$ x > y;
( $76$ points): $x, y \leq 99999$ x, y \le 99999;
( $99$ points): no additional constraints.