There are $n$ piles of stones; the $i$-th pile contains $a_i$ stones.

Two players take turns making moves. In one move, the current player chooses a pile and removes a positive number of stones $k$ from it. The move is allowed only if the binary representation of $k$ contains at most $m$ ones.

The player who cannot make a move loses. Determine who wins if both players play optimally.

Input

The first line contains a single integer $t$ ($1 \le t \le 10^4$): the number of test cases.

Each test case is described by two lines. The first line contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$, $1 \le m \le 60$): the number of piles and the maximum number of ones allowed in the binary representation of a removed amount.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^{18}$): the sizes of the piles. The sizes are not necessarily distinct.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, print First if the player who moves first wins, and Second otherwise.

Examples

Input 1

3
1 2
7
2 1
5 6
3 2
7 14 21

Output 1

Second
First
Second

Note

In the first test case, $m = 2$, and the only pile contains $7$ stones. The first player cannot take all $7$ stones, because $7 = 111_2$ contains three ones. It can be checked that every allowed move leads to a position in which the second player wins.

In the second test case, the first player can take $2$ stones from the first pile, leaving piles of sizes $3$ and $6$.