function binary_search_recursive(a, value, lo, hi) {
    if (hi < lo)
        return null;
    var mid = Math.floor((lo+hi)/2);
    if (a[mid] > value)
        return binary_search_recursive(a, value, lo, mid-1);
    else if (a[mid] < value)
        return binary_search_recursive(a, value, mid+1, hi);
    else
        return mid;
}