Click button inside selected cell by JavaScript?

var start = document.getElementById('start');
start.focus();
start.style.backgroundColor = '#000';
start.style.color = '#FFF';

function dotheneedful(sibling) {
  if (sibling != null) {
    start.focus();
    start.style.backgroundColor = '';
    start.style.color = '';
    sibling.focus();
    sibling.style.backgroundColor = '#000';
    sibling.style.color = '#FFF';
    start = sibling;
  }
}
document.onkeydown = checkKey;
function checkKey(e) {
  e = e || window.event;
  if (e.keyCode == '38') {
    // up arrow
    var idx = start.cellIndex;
    var nextrow = start.parentElement.previousElementSibling;
    if (nextrow != null) {
      var sibling = nextrow.cells[idx];
      dotheneedful(sibling);
    }
  } else if (e.keyCode == '40') {
    // down arrow
    var idx = start.cellIndex;
    var nextrow = start.parentElement.nextElementSibling;
    if (nextrow != null) {
      var sibling = nextrow.cells[idx];
      dotheneedful(sibling);
    }
  } else if (e.keyCode == '37') {
    // left arrow
    var sibling = start.previousElementSibling;
    dotheneedful(sibling);
  } else if (e.keyCode == '39') {
    // right arrow
    var sibling = start.nextElementSibling;
    dotheneedful(sibling);
  } else if (e.keyCode == '13') {

/// ***click button?***
  }
}

td, input {font-size: 1.5rem; font-family: Arial}
table {border-collapse: collapse; background: #EEE;}
td {border: 3px solid #FFF;}
.bt {padding: 0px; display:block; width: 100%; height: 100%; background: #EEE; border: 1px solid #888; border-radius: 3px;}

<table>
  <tr style="text-align:center">
    <td id="start"><input type='button' class="bt" value='a' onclick="functionA()"/></td>
    <td><input type='button' class="bt" value='b' onclick="functionB()"/></td>
    <td><input type='button' class="bt" value='c' onclick="functionC()"/></td>
  </tr>
  <tr>
    <td><input type='button' class="bt" value='d' onclick="functionD()"/></td>
    <td><input type='button' class="bt" value='e' onclick="functionE()"/></td>
    <td><input type='button' class="bt" value='f' onclick="functionF()"/></td>
  </tr>
</table>