Working version

const cycle = (input) => {
  const arrInput = input.split('');
  const firstLetters = [];
  const lastLetters = [];
  for (let i = 0; i < arrInput.length; i += 1) {
    if (arrInput[i - 1] === ' ' || i === 0) {
      firstLetters.push(arrInput[i]);
    }
  }
  for (let i = arrInput.length - 1; i > 0; i -= 1) {
    if (arrInput[i + 1] === ' ' || i === arrInput.length - 1) {
      lastLetters.push(arrInput[i]);
    }
  }
  lastLetters.reverse();
  let currentLetterIndex = 1;
  let currentLastLetter = lastLetters.length - 1;
  console.log(lastLetters);
  for (let i = 0; i < arrInput.length; i += 1) {
    if (arrInput[i + 1] === ' ') {
      arrInput[i] = lastLetters[currentLastLetter];
      if (currentLastLetter === lastLetters.length - 1) {
        currentLastLetter = 0;
      } else {
        currentLastLetter += 1;
      }
    }
  }
  arrInput[arrInput.length - 1] = lastLetters[1];
  for (let i = 0; i < arrInput.length; i += 1) {
    if (arrInput[i - 1] === ' ' || i === 0) {
      if (currentLetterIndex === firstLetters.length) {
        arrInput[i] = firstLetters[0];
      } else {
        arrInput[i] = firstLetters[currentLetterIndex];
        currentLetterIndex += 1;
      }
    }
  }
  return arrInput.join('');
};