For many students, getting a ticket to The ICPC World Finals is a huge achievement, and The 2019 ICPC Asia Danang Regional Contest is a chance to make their dream come true. For some others, they just like to stretch their brains and solve interesting problems.
We – the scientific committee understand that, and we tried our best to set up a problemset that is interesting and diverse in both topics and difficulty. For a few months, we called for problem proposals from many people and received $a$ easy problems, $b$ medium problems and $c$ hard problems. Using these proposals, we want to create a problemset which:
Consists of exactly $n$ problems,
Has at least $1$ easy problem,
Has at least $1$ medium problem,
Has at least $1$ hard problem.
Your task is to check whether it is possible to create such a problemset using the available problems.
The input contains $4$ integers $a$, $b$, $c$ and $n$ $(0 \le a, b, c \le 10, 1 \le n \le 20)$.
Print ‘YES’ if it is possible to create a problemset satisfying above requirements, and ‘NO’ otherwise.
In the first sample, the committee do not have any easy problem. Thus, they cannot create a problemset with at least $1$ easy problem.
In the second sample, the committee can use $3$ easy problems, $7$ medium problems and $3$ hard problems to create a problemset with exactly $13$ problems.
|Sample Input 1||Sample Output 1|
0 3 3 5
|Sample Input 2||Sample Output 2|
4 10 6 13