One day, Bob planted a bean in his backyard and was shocked to see a beanstalk start to grow instantly! The beanstalk grew with incredible speed, and seemed to be reaching for a castle in the clouds. Bob immediately started to climb the beanstalk, as it was growing. Bob can climb $$$k$$$ meters upward per minute. Beginning at the start of minute $$$1$$$, the beanstalk will grow for $$$n$$$ minutes until it reaches the castle in the clouds. At the start of the $$$i$$$th minute, the beanstalk will instantly grow $$$b_i$$$ meters. How many minutes will it take Bob to reach the castle in the clouds? If Bob reaches the top before the end of a minute, round up.
The first line will contain the integers $$$n$$$ $$$(1 \leq n \leq 1000)$$$ and $$$k$$$ $$$(1 \leq k \leq 1000)$$$ – the number of minutes the beanstalk will be growing and the number of meters Bob can climb per second.
The next line will contain $$$n$$$ integers, each representing the number of meters $$$b_i$$$ $$$(1 \leq b_i \leq 1000)$$$ the beanstalk will grow at the start of the $$$i$$$th minute.
Output a single integer – the number of minutes it will take Bob to reach the castle in the clouds.
5 32 2 8 12 15
14
In the sample test:
At the start of minute $$$1$$$, the beanstalk grows to height $$$2$$$. Bob climbs $$$2$$$ meters, then waits until the end of the minute for the beanstalk to grow again.
At the start of minute $$$2$$$, the beanstalk grows to height $$$4$$$. Bob climbs to meter $$$4$$$, then waits until the end of the minute for the beanstalk to grow again.
At the start of minute $$$3$$$, the beanstalk grows to height $$$12$$$. Bob climbs to meter $$$7$$$.
At the start of minute $$$4$$$, the beanstalk grows to height $$$24$$$. Bob climbs to meter $$$10$$$.
At the start of minute $$$5$$$, the beanstalk grows to height $$$39$$$. Bob climbs to meter $$$13$$$.
From minutes $$$6$$$ to $$$14$$$, Bob climbs to meter $$$39$$$.
