H. Enough Cupcakes?
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

After a long day of preparing everything for CODEFEM, the organizers decided that everyone deserved a cupcake.

There are $$$N$$$ tables at the event. At table $$$i$$$, there are $$$a_i$$$ people sitting.

The organizers bought $$$C$$$ cupcakes, and every person should receive exactly one cupcake.

Determine whether there are enough cupcakes for everyone.

  • If there are enough cupcakes, print YES followed by the number of cupcakes remaining.
  • Otherwise, print NO followed by the number of additional cupcakes needed.
Input

The first line contains two integers $$$N$$$ and $$$C$$$ ($$$1 \le N \le 100$$$, $$$0 \le C \le 10^9$$$), representing the number of tables and the number of available cupcakes.

The second line contains $$$N$$$ integers $$$a_1, a_2, \ldots, a_N$$$ ($$$1 \le a_i \le 10^6$$$), where $$$a_i$$$ is the number of people sitting at the $$$i$$$-th table.

Output

If $$$C$$$ is greater than or equal to the total number of people, print YES $$$x$$$, where $$$x$$$ is the number of cupcakes remaining.

Otherwise, print NO $$$x$$$, where $$$x$$$ is the number of additional cupcakes needed.

Examples
Input
4 20
3 5 4 2
Output
YES 6
Input
3 10
4 5 3
Output
NO 2
Note

Example 1.

There are $$$3 + 5 + 4 + 2 = 14$$$ people in total.

Since there are $$$20$$$ cupcakes, $$$20 - 14 = 6$$$ cupcakes remain. Therefore, the output is YES 6.

Example 2.

There are $$$4 + 5 + 3 = 12$$$ people in total.

Since only 10 cupcakes are available, $$$12 - 10 = 2$$$ additional cupcakes are needed. Therefore, the output is NO 2.