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**Input File:** `drivein.txt`

**Output File:** `driveout.txt`

**Time Limit:** 1.2 seconds

**Memory Limit:** 10 Mb

You work for a large software company, and your business is operating systems. "No machine too fast," as you say, "we can always give it something more to do!"

With lawsuits alleging that your operating system is unfairly bundled
with your virtual toast maker and your electronic encyclopedia of
witchcraft, you need to distract the public's attention with a flashy
new product. Unfortunately, lawsuits are expensive and so you have had
to fire all of your technical staff, leaving you with a company of
marketers and managers. After much soul-searching you have hit on a
slogan for your new operating system: *Divide and Conquer!*

In line with your new slogan, your new operating system will partition each hard drive into lots and lots of little pieces. The more partitions, the faster the operating system! You are in charge of designing the advertising brochure, and so you need to know just how many different partitioning possibilities there are.

Your partitioning software works as follows.

- It will only work with a hard drive containing 2
^{n}blocks for some*n*. Initially the hard drive consists of one large partition. - The software may take a partition of size
*k*>= 2 and split it into two equal partitions of size*k*/2, as illustrated below. - The software may take a partition of size
*k*>= 4 and split it into three consecutive partitions of size*k*/4,*k*/2 and*k*/4 (in that order), as illustrated below. - Each partition must consist of an integer number of blocks — you cannot split a block into smaller pieces.

The following diagram illustrates how these operations can be used to split an 8-block hard drive into consecutive partitions of 1, 1, 4 and 2 blocks.

Your task is, given an integer *n*, to work out how many different ways
a hard drive of 2^{n} blocks can be partitioned.
Note that you are
only counting the final partitionings — if the same partitioning can
be achieved in several different ways using the rules above, you should
only count it once.

As an example, the six different ways of
partitioning a hard drive of size 2^{2} = 4
are illustrated below.

Since your colleagues who are proofreading the advertising brochure
cannot deal with large numbers, your program must output the answer modulo
*m* for some modulus *m* <= 1000.
For example, there are 2350
possible partitionings for a hard drive of size
2^{4} = 16. If *m* = 100,
your program would output the answer 50 in this case.

Hint:

The numbers in this problem can grow extremely large, and so it is recommended that you avoid overflow by reducing modulomduring some of your intermediate calculations. For example, instead ofa=b^{5}modm, you could evaluatea= ((b^{3}modm) x (b^{2}modm)) modm.

You can evaluatekmodmin C/C++ by writingk % m, and in Pascal you can writek mod m.

Input will consist of a single line containing the integers *n*
and *m*
as described above, separated by a single space.
You are guaranteed that
0 <= *n* <= 10,000,000 and
1 <= *m* <= 1,000.

Output should consist of a single integer, giving the number of
partitionings reduced modulo *m* as described above.

2 100

6

4 100

50

The score for each input scenario will be 100% if the correct answer is written to the output file, and 0% otherwise.

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