Problem A
Moscow Dream

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.

Input

The input contains $4$ integers $a$, $b$, $c$ and $n$ $(0\le a,b,c\le 10,1\le n\le 20)$.

Output

Print ‘YES’ if it is possible to create a problemset satisfying above requirements, and ‘NO’ otherwise.

Explanation of sample data

• 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.

0 3 3 5

NO

4 10 6 13

YES