H. Hero Morethor
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

According to historical evidence, it is believed that in ancient Nlogonia, all citizens lived in peace and harmony, confident that they were protected from any enemy thanks to a powerful hero: Morethor. The god Hadesoko, known for his terrifying monsters, constantly sought to torment humanity, but our hero prevented his evil deeds. However, recent discoveries point to a period of darkness: after Morethor's encounter with the god Promethilio, our hero went missing for a long time, allowing Hadesoko to invade the lands of our ancestors. We know that Morethor reappeared at some point in the past and immediately began hunting the monsters sent by Hadesoko and facing them in the order they were encountered. However, despite the collected data, researchers have not yet been able to conclude whether Morethor defeated all the forces of evil or if he failed in his mission. Thus, they have asked for your help to evaluate the data and resolve this great doubt!

Given Morethor's ability $$$H$$$ right after his return, determine if he is capable of facing all $$$N$$$ monsters from Hadesoko. The $$$i$$$-th encountered monster has a strength $$$F_i$$$. Morethor faces only one monster at a time and is able to defeat it if his current ability is greater than or equal to the monster's strength. If our hero wins the battle, he acquires the strength of his opponent (meaning he adds the monster's strength to his ability). Otherwise, he is defeated.

Input

The first line contains an integer $$$N$$$ ($$$0 \le N \le 10^5$$$) and an integer $$$H$$$ ($$$0 \le H \le 10^4$$$) — the number of monsters and the hero's initial ability, respectively.

The second line contains $$$N$$$ integers $$$F_i$$$ ($$$0 \le F_i \le 10^4$$$) — the $$$i$$$-th monster's strength.

Output

Print "SIM" (without quotes) if the hero is able to fight all the monsters, and "NAO" (without quotes) otherwise.

Examples
Input
5 10
1 2 3 4 5
Output
SIM
Input
4 1
1 2 4 8
Output
SIM
Input
4 7
1 1 1 11
Output
NAO
Note

In the second example, the hero starts with an ability of 1, being capable of defeating the first monster and increasing his ability to 2. In the second battle, he is also able to defeat the monster and his ability becomes 4. The same happens in the third and fourth battles, with our hero being able to face all the monsters.