Putting Candies

AtCoder

IDabc241_e

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A=(A_0,A_1,\ldots,A_{N-1})$ of length $N$. There is an initially empty dish. Takahashi is going to repeat the following operation $K$ times. * Let $X$ be the number of candies on the dish. He puts $A_{(X\bmod N)}$ more candies on the dish. Here, $X\bmod N$ denotes the remainder when $X$ is divided by $N$. Find how many candies are on the dish after the $K$ operations. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq K \leq 10^{12}$ * $1 \leq A_i\leq 10^6$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_0$ $A_1$ $\ldots$ $A_{N-1}$ [samples]

Samples

Input #1

5 3
2 1 6 3 1

Output #1

11

The number of candies on the dish transitions as follows.

*   In the $1$\-st operation, we have $X=0$, so $A_{(0\mod 5)}=A_0=2$ more candies will be put on the dish.
*   In the $2$\-nd operation, we have $X=2$, so $A_{(2\mod 5)}=A_2=6$ more candies will be put on the dish.
*   In the $3$\-rd operation, we have $X=8$, so $A_{(8\mod 5)}=A_3=3$ more candies will be put on the dish.

Thus, after the $3$ operations, there will be $11$ candies on the dish. Note that you must **not** print the remainder divided by $N$.

Input #2

10 1000000000000
260522 914575 436426 979445 648772 690081 933447 190629 703497 47202

Output #2

826617499998784056

The answer may not fit into a $32$\-bit integer type.

API Response (JSON)

{
  "problem": {
    "name": "Putting Candies",
    "description": {
      "content": "You are given a sequence $A=(A_0,A_1,\\ldots,A_{N-1})$ of length $N$.   There is an initially empty dish. Takahashi is going to repeat the following operation $K$ times. *   Let $X$ be the number of c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc241_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A=(A_0,A_1,\\ldots,A_{N-1})$ of length $N$.  \nThere is an initially empty dish. Takahashi is going to repeat the following operation $K$ times.\n\n*   Let $X$ be the number of c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments