Problem statement

The spellbook you have contains $ N $ of spells.

Magic is numbered from $ 1 $ to $ N $, and the cost of magic $i (1 \ le i \ le N)$ is initially an integer $ A_i $.

Your goal is to cast all the spells in the spellbook $ 1 $ each.

You can eat $ K $ of cookies before you start casting magic. It doesn't take long to eat cookies.

For every $ 1 $ you eat a cookie, you can choose a magic with a positive cost of $ 1 $ and reduce that cost by $ 1 $.

After eating the cookie, you start casting magic.

Your MP is initially $ M $. You repeat either of the following to cast $ N $ of magic $ 1 $ in any order.

• Choose an integer $i (1 \ le i \ le N)$ for $ 1 $ and cast the magical $ i $. However, the current MP must cost more than the magical $ i $.
• Time does not elapse.
• Consume MP for the cost of magical $ i $.
• Rest. However, if the current MP is $ m $, then $ m <M $ must be.
• Time elapses $ M --m $.
• Recover $ 1 $ MP.

Find the minimum amount of time it will take you to cast $ N $ of spells $ 1 $ each in any order.

Constraint

• $1 \ leq N \ leq 10 ^ 5$
• $1 \ leq M \ leq 10 ^ 6$
• $0 \ leq K \ leq \ sum_ {i = 1} ^ {N} A_i$
• $1 \ leq A_i \ leq M$
• All inputs are integers.

input

Input is given from standard input in the following format.

$ N $ $ M $ $ K $
$ A_1 $ $ A_2 $ $\$ $ A_N $

output

Print the minimum amount of time it takes to cast $ N $ of magic $ 1 $ each.

Input example 1

2 4 0
twenty four

Output example 1

3

Since the cost of any magic cannot be reduced, I will continue to cast magic as it is.

• First, cast the magic $ 1 $. It consumes $ 2 $ of MP, so the remaining MP is $ 4-2 = 2 $.

You cannot cast magic $ 2 $ as it is because you need $ 4 $ MP to cast magic $ 2 $.

• I'll take a rest. Time elapses $ 4-2 = 2 $ seconds. It recovers $ 1 $ of MP, so the remaining MP is $ 2 + 1 = 3 $.
• I'll take a rest. Time elapses $ 4-3 = 1 $ seconds. It recovers $ 1 $ of MP, so the remaining MP is $ 3 + 1 = 4 $.
• Cast magic $ 2 $. It consumes $ 4 $ of MP, so the remaining MP is $ 4-4 = 0 $.

From the above, if the time is $ 2 + 1 = 3 $ seconds, the magic $ 1,2 $ can be cast $ 1 $ each time. You can't cast all the spells in less time, so the answer you're looking for is $ 3 $.

Input example 2

3 9 6
2 3 9

Output example 2

0

With a final magic cost of $ 2, 2, 4 $, you can cast all the magic without a break.

Input example 3

3 16 2
6 9 9

Output example 3

twenty one

Input example 4

2 1000000 0
1000000 1000000

Output example 4

500000500000

The answer may not fit in the range that can be represented by a 32-bit integer.

Example

Input

2 4 0
2 4

Output

3

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