Rishi and his gang of wizards are hunting the Radiant Sky Pheonix, a legendary bird they're sure will make for a good kebab. Since the phoenix is a magical creature, the wizards must use magical attacks to defeat it.

There are ~n~ wizards, each with a power ~p_i~. To launch an attack on the phoenix, the wizards combine all their powers using a bitwise OR to obtain a total power ~p_t~. For the attack to succeed, ~p_t~ must be at least ~x~.

However, these attacks are tiring! After each attack, exactly one bit from exactly one of the wizards' powers must change from set to unset (~1 \rightarrow 0~). For example, if a wizard has a power of ~11~ (1011 in binary), then their power could change to ~10~ (1010), ~9~ (1001) or ~3~ (0011) after an attack. The wizards get to choose who loses a bit, and which bit is cleared.

Assuming the wizards play optimally, determine the maximum number of attacks they can perform on the phoenix before their combined power falls below ~x~.

Input

The first line contains a two integers, ~n~ and ~x~ ~(1 \leq n, x \leq 2026)~, the number of wizards in Rishi's gang, and the power needed to make a successful attack.

The second line contains ~n~ integers, ~p_1, \dots, p_n~ (~1 \leq p_i \leq 2026~), where ~p_i~ is the power of the ~i~th wizard.

Output

Output the maximum number of attacks the wizards can make, while their power stays above ~x~.

Example

Input 1

3 10
11 9 4

Output 1

5

The wizards can make 5 attacks in total. Below is one way they could achieve this, although it is not the only way.

Initial State:
Wizard 1: 11    (1011)
Wizard 2: 9     (1001)
Wizard 3: 4     (0100)
Total Power: 15 (1111)

After Attack 1:
Wizard 1: 10    (1010) [lost fourth bit]
Wizard 2: 9     (1001)
Wizard 3: 4     (0100)
Total Power: 15 (1111)

After Attack 2:
Wizard 1: 2     (0010) [lost first bit]
Wizard 2: 9     (1001)
Wizard 3: 4     (0100)
Total Power: 15 (1111)

After Attack 3:
Wizard 1: 2     (0010)
Wizard 2: 8     (1000) [lost fourth bit]
Wizard 3: 4     (0100)
Total Power: 14 (1110)

After Attack 4:
Wizard 1: 2     (0010)
Wizard 2: 8     (1000)
Wizard 3: 0     (0000) [lost second bit]
Total Power: 10 (1010)

After Attack 5:
Wizard 1: 0     (0000) [lost third bit]
Wizard 2: 8     (1000)
Wizard 3: 0     (0000)
Total Power: 8  (1000)

Input 2

8 7
1 2 3 4 5 6 7 8

Output 2

13

Input 3

14 10
1 2 3 4 5 6 7 1 2 3 4 5 6 7

Output 3

0