Problem:
Score : 500 points

Problem Statement

A robot is put at the origin in a two-dimensional plane.
Initially, the robot is facing in the positive x-axis direction.

This robot will be given an instruction sequence s.
s consists of the following two kinds of letters, and will be executed in order from front to back.

F : Move in the current direction by distance 1.

T : Turn 90 degrees, either clockwise or counterclockwise.

The objective of the robot is to be at coordinates (x, y) after all the instructions are executed.
Determine whether this objective is achievable.

Constraints

s consists of F and T.

1 \leq |s| \leq 8 000

x and y are integers.

|x|, |y| \leq |s|

Input

Input is given from Standard Input in the following format:

s
x y

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

FTFFTFFF
4 2

Sample Output 1

Yes

The objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.

Sample Input 2

FTFFTFFF
-2 -2

Sample Output 2

Yes

The objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.

Sample Input 3

FF
1 0

Sample Output 3

No

Sample Input 4

TF
1 0

Sample Output 4

No

Sample Input 5

FFTTFF
0 0

Sample Output 5

Yes

The objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.

Sample Input 6

TTTT
1 0

Sample Output 6

No

Solution in Scala (2.11.7) (judge verdict: Accepted)

import scala.io.{StdIn => in}
import scala.collection.{mutable => mu}

object Main extends App {
  val s = in.readLine
  val Array(x, y) = in.readLine.split(" ").map(_.toInt)
  val bufX = mu.ArrayBuffer.empty[Int]
  val bufY = mu.ArrayBuffer.empty[Int]
  val (coordX, coordY) = {
    var cnt = 0
    var isEven = true
    bufX += 0
    s.foreach(ch => {
      if(ch == 'T') {
        isEven = isEven ^ true
        if(isEven) {
          bufX += 0
          cnt += 1
        }
        else {
          bufY += 0
        }
      }
      else {
        if(isEven) bufX(cnt) += 1
        else bufY(cnt) += 1
      }
    })
    (bufX.sum, bufY.sum)
  }
  // debug("x:", bufX.mkString(" "))
  // debug("y:", bufY.mkString(" "))

  val corr = (coordX + coordY) * 2 + 10 //座標のマイナスを補正する
  val coordMax = 2 * corr + 10
  // debug("corr", corr)
  val x2 = x + corr
  val y2 = y + corr
  // テーブル構築 : dp(i)(j)でi回目の操作で座標軸上の n + corr に居られるか
  val dpx = Array.ofDim[Boolean](bufX.size + 1, coordMax)
  val dpy = Array.ofDim[Boolean](bufY.size + 1, coordMax)
  dpx(0)(corr) = true
  dpy(0)(corr) = true

  // 最初の向きは固定
  if(dpx.size > 1) {
    dpx(1)(corr + bufX(0)) = true
    // debug("dpx:", 1, bufX(0))
  }

  for{
    i <- 1 until bufX.size
    j <- 0 until coordMax
  } {
    if(dpx(i)(j)) {
      // debug("dpx:", i+1,j-bufX(i),j+bufX(i))
      if(j - bufX(i) >= 0) dpx(i+1)(j-bufX(i)) = true
      if(j + bufX(i) >= 0) dpx(i+1)(j+bufX(i)) = true
    }
  }
  for{
    i <- 0 until bufY.size
    j <- 0 until coordMax
  } {
    if(dpy(i)(j)) {
      // debug("dpy:", i, j, i+1,j-bufY(i),j+bufY(i))
      if(j - bufY(i) >= 0) dpy(i+1)(j-bufY(i)) = true
      if(j + bufY(i) >= 0) dpy(i+1)(j+bufY(i)) = true
    }
  }

  // debug(dpx.size, dpy.size)
  // debug(bufX.size, x2, bufY.size, y2)
  val ans = if(dpx(bufX.size)(x2) && dpy(bufY.size)(y2)) "Yes" else "No"
  println(ans)

  def debug(any:Any*):Unit = {
    if(this.getClass.toString == "class Main$") return
    println(any.mkString(" "))
  }
}