D. Uniq

Given N strings, count the number of different strings.

The strings will be generated by a pseudo random number generator, so you don't have to worry about downloading and parsing large text files.

A string is represented by a sequence of integers. The first integer is the number of characters in the string, each one of the following integers encode a character of the string. Such integer sequences can be concatenated to represent multiple strings.

The integer sequence representing the given N strings is generated by the following linear congruential generator:

X := SEED
A := 8433437992146984169
B := 7905438737954111703

function nextinteger():
	X := (A*X + B) mod (2^64)
	return X / (2^56)

where ^, / and mod are exponentiation, integer division and modulo operations with the usual semantics.

Input

A single line containing two integers: N and SEED.

Output

The number of different strings.

Example input

4 11413960417

Example output

3

Random numbers are 2, 245, 71, 1, 46, 4, 105, 177, 135, 114, 1, 46, 154, 195, ...
The lengths of the four strings are 2, 1, 4, 1.