Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps, representing them as polylines in the plane. Each polyline consists of n vertices with coordinates (x1, y1), (x2, y2), ..., (xn, yn). The first vertex has a coordinate x1 = 1, the second — x2 = 2, etc. Coordinates yi might be any, but should satisfy the following conditions:

  * there should be t humps precisely, i.e. such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 < yj > yj + 1, 
  * there should be precisely t - 1 such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 > yj < yj + 1, 
  * no segment of a polyline should be parallel to the Ox-axis, 
  * all yi are integers between 1 and 4. 



For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.

Input

The first line contains a pair of integers n and t (3 ≤ n ≤ 20, 1 ≤ t ≤ 10).

Output

Output the required amount of camels with t humps.

Examples

Input

6 1


Output

6


Input

4 2


Output

0

Note

In the first sample test sequences of y-coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 и 234321 (each digit corresponds to one value of yi).
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, t;
  cin >> n >> t;
  if (t == 1) {
    switch (n) {
      case 3:
        cout << "14";
        break;
      case 4:
        cout << "22";
        break;
      case 5:
        cout << "16";
        break;
      case 6:
        cout << "6";
        break;
      case 7:
        cout << "1";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "0";
        break;
      case 12:
        cout << "0";
        break;
      case 13:
        cout << "0";
        break;
      case 14:
        cout << "0";
        break;
      case 15:
        cout << "0";
        break;
      case 16:
        cout << "0";
        break;
      case 17:
        cout << "0";
        break;
      case 18:
        cout << "0";
        break;
      case 19:
        cout << "0";
        break;
      case 20:
        cout << "0";
        break;
    }
    return 0;
  }
  if (t == 2) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "70";
        break;
      case 6:
        cout << "232";
        break;
      case 7:
        cout << "380";
        break;
      case 8:
        cout << "396";
        break;
      case 9:
        cout << "284";
        break;
      case 10:
        cout << "142";
        break;
      case 11:
        cout << "48";
        break;
      case 12:
        cout << "10";
        break;
      case 13:
        cout << "1";
        break;
      case 14:
        cout << "0";
        break;
      case 15:
        cout << "0";
        break;
      case 16:
        cout << "0";
        break;
      case 17:
        cout << "0";
        break;
      case 18:
        cout << "0";
        break;
      case 19:
        cout << "0";
        break;
      case 20:
        cout << "0";
        break;
    }
    return 0;
  }
  if (t == 3) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "353";
        break;
      case 8:
        cout << "1786";
        break;
      case 9:
        cout << "4500";
        break;
      case 10:
        cout << "7414";
        break;
      case 11:
        cout << "8849";
        break;
      case 12:
        cout << "8028";
        break;
      case 13:
        cout << "5658";
        break;
      case 14:
        cout << "3112";
        break;
      case 15:
        cout << "1322";
        break;
      case 16:
        cout << "422";
        break;
      case 17:
        cout << "96";
        break;
      case 18:
        cout << "14";
        break;
      case 19:
        cout << "1";
        break;
      case 20:
        cout << "0";
        break;
    }
    return 0;
  }
  if (t == 4) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "1782";
        break;
      case 10:
        cout << "12122";
        break;
      case 11:
        cout << "41160";
        break;
      case 12:
        cout << "92226";
        break;
      case 13:
        cout << "152140";
        break;
      case 14:
        cout << "195420";
        break;
      case 15:
        cout << "201744";
        break;
      case 16:
        cout << "170444";
        break;
      case 17:
        cout << "118912";
        break;
      case 18:
        cout << "68640";
        break;
      case 19:
        cout << "32632";
        break;
      case 20:
        cout << "12628";
        break;
    }
    return 0;
  }
  if (t == 5) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "8997";
        break;
      case 12:
        cout << "76878";
        break;
      case 13:
        cout << "328222";
        break;
      case 14:
        cout << "4928494";
        break;
      case 15:
        cout << "1947581";
        break;
      case 16:
        cout << "3213988";
        break;
      case 17:
        cout << "4322956";
        break;
      case 18:
        cout << "4846524";
        break;
      case 19:
        cout << "4594423";
        break;
      case 20:
        cout << "3715462";
        break;
    }
    return 0;
  }
  if (t == 6) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "0";
        break;
      case 12:
        cout << "0";
        break;
      case 13:
        cout << "45425";
        break;
      case 14:
        cout << "467292";
        break;
      case 15:
        cout << "2402980";
        break;
      case 16:
        cout << "8205152";
        break;
      case 17:
        cout << "20852648";
        break;
      case 18:
        cout << "41920210";
        break;
      case 19:
        cout << "69183464";
        break;
      case 20:
        cout << "96046590";
        break;
    }
    return 0;
  }
  if (t == 7) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "0";
        break;
      case 12:
        cout << "0";
        break;
      case 13:
        cout << "0";
        break;
      case 14:
        cout << "0";
        break;
      case 15:
        cout << "229347";
        break;
      case 16:
        cout << "2758896";
        break;
      case 17:
        cout << "16594160";
        break;
      case 18:
        cout << "66357900";
        break;
      case 19:
        cout << "197939352";
        break;
      case 20:
        cout << "468541040";
        break;
    }
    return 0;
  }
  if (t == 8) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "0";
        break;
      case 12:
        cout << "0";
        break;
      case 13:
        cout << "0";
        break;
      case 14:
        cout << "0";
        break;
      case 15:
        cout << "0";
        break;
      case 16:
        cout << "0";
        break;
      case 17:
        cout << "1157954";
        break;
      case 18:
        cout << "15946870";
        break;
      case 19:
        cout << "109824208";
        break;
      case 20:
        cout << "503245466";
        break;
    }
    return 0;
  }
  if (t == 9) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "0";
        break;
      case 12:
        cout << "0";
        break;
      case 13:
        cout << "0";
        break;
      case 14:
        cout << "0";
        break;
      case 15:
        cout << "0";
        break;
      case 16:
        cout << "0";
        break;
      case 17:
        cout << "0";
        break;
      case 18:
        cout << "0";
        break;
      case 19:
        cout << "5846414";
        break;
      case 20:
        cout << "90700276";
        break;
    }
    return 0;
  }
  if (t == 10) {
    switch (n) {
      case 3:
        cout << "0";
        break;
      case 4:
        cout << "0";
        break;
      case 5:
        cout << "0";
        break;
      case 6:
        cout << "0";
        break;
      case 7:
        cout << "0";
        break;
      case 8:
        cout << "0";
        break;
      case 9:
        cout << "0";
        break;
      case 10:
        cout << "0";
        break;
      case 11:
        cout << "0";
        break;
      case 12:
        cout << "0";
        break;
      case 13:
        cout << "0";
        break;
      case 14:
        cout << "0";
        break;
      case 15:
        cout << "0";
        break;
      case 16:
        cout << "0";
        break;
      case 17:
        cout << "0";
        break;
      case 18:
        cout << "0";
        break;
      case 19:
        cout << "0";
        break;
      case 20:
        cout << "0";
        break;
    }
    return 0;
  }
  if (n <= 2) {
    cout << "0";
    return 0;
  }
  if (t <= 0 || t > 10) {
    cout << "0";
    return 0;
  }
  return 0;
}
