write a go solution for Description:
You are given integers d and p, p is prime.

Also you have a mysterious device. It has memory cells, each contains an integer between 0 and p-1. Also two instructions are supported, addition and raising to the d-th power. textbfBotharemodulo p.

The memory cells are numbered 1,2,...,5000. Initially cells 1 and 2 contain integers x and y, respectively (0<=slantx,y<=p-1). All other cells contain textbf1s.

You can not directly access values in cells, and you textbfdon'tknow values of x and y (but you know they are written in first two cells). You mission, should you choose to accept it, is to write a program using the available instructions to obtain the product xy modulo p in one of the cells. You program should work for all possible x and y.

Addition instruction evaluates sum of values in two cells and writes it to third cell. This instruction is encoded by a string "+ e1 e2 to", which writes sum of values in cells e1 and e2 into cell to. Any values of e1, e2, to can coincide.

Second instruction writes the d-th power of a value in some cell to the target cell. This instruction is encoded by a string "^ e to". Values e and to can coincide, in this case value in the cell will be overwritten.

Last instruction is special, this is the return instruction, and it is encoded by a string "f target". This means you obtained values xybmodp in the cell target. No instructions should be called after this instruction.

Provide a program that obtains xybmodp and uses no more than 5000 instructions (including the return instruction).

It is guaranteed that, under given constrains, a solution exists.

Input Format:
The first line contains space-separated integers d and p (2<=slantd<=slant10, d<p, 3<=qslantp<=qslant10^9+9, p is prime).

Output Format:
Output instructions, one instruction per line in the above format. There should be no more than 5000 lines, and the last line should be the return instruction.

Note:
This problem has no sample tests. A sample output is shown below. Note that this output is not supposed to be a solution to any testcase, and is there purely to illustrate the output format.

texttt+113texttt^33texttt+322texttt+323texttt^31textttf1

Here's a step-by-step runtime illustration:

beginarray|c|c|c|c|hlinetexttt&cell1&cell2&cell3hlineinitially&x&y&1hlinetexttt+113&x&y&2xhlinetexttt^33&x&y&(2x)^dhlinetexttt+322&x&y+(2x)^d&(2x)^dhlinetexttt+323&x&y+(2x)^d&y+2*(2x)^dhlinetexttt^31&(y+2*(2x)^d)^d&y+(2x)^d&y+2*(2x)^dhlineendarray

Suppose that d=2 and p=3. Since for x=0 and y=1 the returned result is 1neq0*1bmod3, this program would be judged as incorrect.. Output only the code with no comments, explanation, or additional text.