D. Berland Fair
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

XXI Berland Annual Fair is coming really soon! Traditionally fair consists of $$$n$$$ booths, arranged in a circle. The booths are numbered $$$1$$$ through $$$n$$$ clockwise with $$$n$$$ being adjacent to $$$1$$$. The $$$i$$$-th booths sells some candies for the price of $$$a_i$$$ burles per item. Each booth has an unlimited supply of candies.

Polycarp has decided to spend at most $$$T$$$ burles at the fair. However, he has some plan in mind for his path across the booths:

  • at first, he visits booth number $$$1$$$;
  • if he has enough burles to buy exactly one candy from the current booth, then he buys it immediately;
  • then he proceeds to the next booth in the clockwise order (regardless of if he bought a candy or not).

Polycarp's money is finite, thus the process will end once he can no longer buy candy at any booth.

Calculate the number of candies Polycarp will buy.


The first line contains two integers $$$n$$$ and $$$T$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le T \le 10^{18}$$$) — the number of booths at the fair and the initial amount of burles Polycarp has.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the price of the single candy at booth number $$$i$$$.


Print a single integer — the total number of candies Polycarp will buy.

3 38
5 2 5
5 21
2 4 100 2 6

Let's consider the first example. Here are Polycarp's moves until he runs out of money:

  1. Booth $$$1$$$, buys candy for $$$5$$$, $$$T = 33$$$;
  2. Booth $$$2$$$, buys candy for $$$2$$$, $$$T = 31$$$;
  3. Booth $$$3$$$, buys candy for $$$5$$$, $$$T = 26$$$;
  4. Booth $$$1$$$, buys candy for $$$5$$$, $$$T = 21$$$;
  5. Booth $$$2$$$, buys candy for $$$2$$$, $$$T = 19$$$;
  6. Booth $$$3$$$, buys candy for $$$5$$$, $$$T = 14$$$;
  7. Booth $$$1$$$, buys candy for $$$5$$$, $$$T = 9$$$;
  8. Booth $$$2$$$, buys candy for $$$2$$$, $$$T = 7$$$;
  9. Booth $$$3$$$, buys candy for $$$5$$$, $$$T = 2$$$;
  10. Booth $$$1$$$, buys no candy, not enough money;
  11. Booth $$$2$$$, buys candy for $$$2$$$, $$$T = 0$$$.

No candy can be bought later. The total number of candies bought is $$$10$$$.

In the second example he has $$$1$$$ burle left at the end of his path, no candy can be bought with this amount.