Problem Statement

A Kadomatsu sequence is defined as follows: when three integers are arranged as $A$, $B$, $C$ from the left,
all the values are distinct and the second largest integer among $A$, $B$, $C$ is either $A$ or $C$.

Also, when three integers form a Kadomatsu sequence, their Kadomatsu points are the maximum value among the three integers.

You are given $N$ triples of three positive integers $A$, $B$, $C$, in this order from the left.
You may perform, up to $N$ times, an operation that swaps only the middle positive integers $B$ between any two triples.
Determine whether all the triples can be made into Kadomatsu sequences by the operations.
If they can, determine whether the sum of the Kadomatsu points of all the triples can be made at least $M$ points.

Input

$N$ $M$
$A_1$ $B_1$ $C_1$
$A_2$ $B_2$ $C_2$
$ \vdots\ $
$A_N$ $B_N$ $C_N$

$N$ is the number of given triples of three positive integers $A$, $B$, $C$. $1 \le N \le 3000$.
$M$ is the number of points used for the determination in the problem statement. $0 \le M \le 3000000000000 = 3 \times 10^{12}$.
$A_i$, $B_i$, $C_i$ are the positive integers $A$, $B$, $C$ of the $i$-th given triple. $A_i \neq C_i$. $1 \le A_i,B_i,C_i \le 1000000000 = 10^9$.

Output

If not all the triples can be made into Kadomatsu sequences, output "NO" on a single line only.
If all the triples can be made into Kadomatsu sequences, output "YES" on the first line.
If all the triples can be made into Kadomatsu sequences and the sum of the Kadomatsu points can be made at least $M$ points, output "KADOMATSU!" on the second line.
If all the triples can be made into Kadomatsu sequences but the sum of the Kadomatsu points cannot be made at least $M$ points, output "NO" on the second line.

Sample

2 5
2 3 4
1 1 2

YES
KADOMATSU!

3 20
7 5 5
2 8 1
4 3 5

YES
KADOMATSU!

1 100
2 1 3

YES
NO

2 0
1 2 3
4 1 3

NO

5 2021
5 10 1
3 3 16
7 8 8
11 1979 15
6 8 9

YES
KADOMATSU!