Joe’s Water Corporation

Joe's Water Corporation is a company that sells bottled water. However, it has competition that also sells bottled water, sometimes at a cheaper price.

If your price is lower, then you get to sell at that store. If not, you lose the chance to sell your water at that store. In the case of a tie, the competition always wins.

You, as the manager of Joe's Water Corporation, can choose to lower the price of water for every single store you own by $M$ dollars. This could lead to higher revenue (if the discount results in your water being sold at more stores) or lower revenue (if the lower prices outweigh the higher number of locations the water is sold in.) You should print out YES if it makes you more revenue, or NO if it makes you less revenue / same revenue.

note

The revenue is defined as the sum of the prices at the stores at which your company sells water at a lower price than that of the competitor.

Input

• On the first line, a list of integers delimited by spaces, representing the prices you set for each store.
• On the second line, a list of integers delimited by spaces, representing the prices the competing company set for each store.
• On the third line, an integer $M$ indicating a discount you can apply to all your prices.

The number of stores is guaranteed to be the same.

Output

Output a single string denoting whether applying the discount would result in higher profits: either YES or NO. If the profit does not change, output NO.

Examples

Example 1

Input

3 4 6 2 5 6
4 2 2 3 6 5
2

Output

NO

Explanation

Originally, in the $1^{st}$, $4^{th}$, and $5^{th}$ stores we have strictly lower prices than our competitor. Therefore our original profit is $3 + 2 + 5 = 10$ dollars.

By reducing the price by $2$, we get the following prices:

1 2 4 0 3 4
4 2 2 3 6 5

In the $1^{st}$, $4^{th}$, $5^{th}$ and $6^{th}$ stores we have strictly lower prices than our competitor. Thus our profit after applying the discount is $1 + 0 + 3 + 4 = 8$ dollars.

As $8 <= 10$, applying the discount results in lower profit overall. Thus, the output is NO.

Example 2

Input

4 7 9 3
5 5 9 2
1

Output

YES

Explanation

Our original profit is $4$ dollars, as we only have lower prices than our competitor in the $1^{st}$ store.

By reducing the price by $1$, we get the following prices:

3 6 8 2
5 5 9 2

We have lower prices than our competitor in the $1^{st}$ and $3^{rd}$ stores. Thus our profit after applying the discount is $3 + 8 = 11$ dollars. As $11 > 4$, the output is YES.

Example 3

Input

7
5
2

Output

NO

Explanation

There is only one store, where we have a higher price than our competitor. Thus we make $0$ profit in the beginning. When we apply the discount, our price decreases to $5$. However, as our competitor wins in the case of a tie, we still make $0$ profit. Therefore, as our profit did not change, the output is NO.

Model Solution

Click to reveal

joes_prices = list(map(int, input().split()))
competitors_prices = list(map(int, input().split()))
discount = int(input())

original_profit = 0
discounted_profit = 0

for i in range(len(joes_prices)):
    cur_joe_price = int(joes_prices[i])
    cur_competitor_price = int(competitors_prices[i])
    if cur_joe_price < cur_competitor_price:
        original_profit += cur_joe_price
    if cur_joe_price - discount < cur_competitor_price:
        discounted_profit += cur_joe_price - discount

print("YES" if discounted_profit > original_profit else "NO")

Step-by-step tutorial

Let's begin by reading in the input.

joes_prices = list(map(int, input().split()))
competitors_prices = list(map(int, input().split()))
discount = int(input())

tip

If you are confused about how map is being used above, take a look at the model solution for Joe's Doubling Points!

We will maintain two counters, tracking the original profit and the profit with the discount applied. Then, at the end, we can compare them to obtain the answer.

original_profit = 0
discounted_profit = 0

For each iteration, we store both Joe's and the competitor's price.

for i in range(len(joes_prices)):
    cur_joe_price = joes_prices[i]
    cur_competitor_price = competitors_prices[i]

Then, we update the counters appropriately.

1. If Joe's original price is strictly less than the competitor's price, update original_profit.
2. If Joe's price with the discount applied is strictly less than the competitor's price, update discounted_profit.

if cur_joe_price < cur_competitor_price:
    original_profit += cur_joe_price
if cur_joe_price - discount < cur_competitor_price:
    discounted_profit += cur_joe_price - discount

Finally, after we've compared their prices with and without Joe's discount applied, we can see whether or not it made a difference.

print("YES" if discounted_profit > original_profit else "NO")

tip

true_val if condition else false_val is a ternary conditional statement, allowing simple conditionals to be more concise or "elegant", if you're into that.

Compare this to if we wrote it normally:

if discounted_profit > original_profit:
    print("YES")
else:
    print("NO")