Christmas

AtCoder

IDabc115_d

Time2000ms

Memory256MB

Difficulty—

In some other world, today is Christmas. Mr. Takaha decides to make a multi-dimensional burger in his party. A _level-$L$ burger_ ($L$ is an integer greater than or equal to $0$) is the following thing: * A level-$0$ burger is a patty. * A level-$L$ burger $(L \geq 1)$ is a bun, a level-$(L-1)$ burger, a patty, another level-$(L-1)$ burger and another bun, stacked vertically in this order from the bottom. For example, a level-$1$ burger and a level-$2$ burger look like `BPPPB` and `BBPPPBPBPPPBB` (rotated $90$ degrees), where `B` and `P` stands for a bun and a patty. The burger Mr. Takaha will make is a level-$N$ burger. Lunlun the Dachshund will eat $X$ layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat? ## Constraints * $1 \leq N \leq 50$ * $1 \leq X \leq ($ the total number of layers in a level-$N$ burger $)$ * $N$ and $X$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $X$ [samples]

Samples

Input #1

2 7

Output #1

4

There are $4$ patties in the bottom-most $7$ layers of a level-$2$ burger (`BBPPPBPBPPPBB`).

Input #2

1 1

Output #2

0

The bottom-most layer of a level-$1$ burger is a bun.

Input #3

50 4321098765432109

Output #3

2160549382716056

A level-$50$ burger is rather thick, to the extent that the number of its layers does not fit into a $32$\-bit integer.

API Response (JSON)

{
  "problem": {
    "name": "Christmas",
    "description": {
      "content": "In some other world, today is Christmas. Mr. Takaha decides to make a multi-dimensional burger in his party. A _level-$L$ burger_ ($L$ is an integer greater than or equal to $0$) is the following thin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc115_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In some other world, today is Christmas.\nMr. Takaha decides to make a multi-dimensional burger in his party. A _level-$L$ burger_ ($L$ is an integer greater than or equal to $0$) is the following thin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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