javascriptで日付セレクトボックスを作る #JavaScript

日付チェックボックス
<!DOCTYPE html>
<html>

<head>
    <title>日付選択</title>
    <script>
        //数値カウンターまとめ
        function Counter(elementId, start, end) {
            document.getElementById(elementId).innerHTML = '';
            for (let i = start; i <= end; i++) {
                let option = document.createElement("option");
                option.value = i;
                option.text = i;
                document.getElementById(elementId).appendChild(option);
            }
        }

        //年月はまとめてカウンターに渡して生成
        function showYearCounter(yearId, monthId, dayId) {
            Counter(yearId, 1800, 2020);
            Counter(monthId, 1, 12);
            showdayCounter(yearId, monthId, dayId);
        }

        //日だけ年月で３パターンを判定してカウンター関数に投げる
        function showdayCounter(yearId, monthId, dayId) {
            let year = document.getElementById(yearId).value;
            let month = document.getElementById(monthId).value;
            let februaryDays = leap(year) ? 29 : 28;

            if (month == 2) {
                Counter(dayId, 1, februaryDays);
            } else if (month.match(/^(4|6|9|11)$/)) {
                Counter(dayId, 1, 30);
            } else {
                Counter(dayId, 1, 31);
            }
        }

        //閏年判定
        function leap(year) {
            return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
        }

    </script>
</head>

<body>

    <body onload="showYearCounter('year', 'month', 'day');">
        <select id="year" onchange="showdayCounter('year', 'month', 'day');"></select>年
        <select id="month" onchange="showdayCounter('year', 'month', 'day');"></select>月
        <select id="day"></select>日
    </body>

</html>