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:

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.


A single line containing two integers: N and SEED.


The number of different strings.

Example input

4 11413960417

Example output


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.