[Alexandroppolus]

function getCount(n, k) {
    if (k < 1) return 0;
    const map = new Map();

    function calc(f, n, k) {
        if (n < f * k || n > 9 * k) {
            return 0;
        }
        if (k < 2) {
            return 1;
        }
        const key = `${f}_${n}_${k}`;
        const saved = map.get(key);
        if (saved != null) { return saved; }

        let count = 0;

        for (let i = f; i <= 9; ++i) {
            count += calc(i, n - i, k - 1);
        }

        map.set(key, count);

        return count;
    }

    return calc(1, n, k);
}

function getMin(n, k) {
    if (k < 1 || n < k || n > 9 * k) {
        return 0;
    }
    let r = 0;
    while (k > 1 && n - 1 <= 9 * (k - 1)) {
        r = r * 10 + 1;
        n--;
        k--;
    }
    k--;
    r = r * 10 + n - 9 * k;
    while (k > 0) {
        r = r * 10 + 9;
        k--;
    }
    return r;
}

function getMax(n, k) {
    if (k < 1 || n < k || n > 9 * k) {
        return 0;
    }
    const base = Math.floor(n / k);
    const head = k - n % k;
    let r = 0;
    for (i = 0; i < k; ++i) {
        r = r * 10 + base + (i < head ? 0 : 1);
    }
    return r;
}

function luckyNumbers(n, k) {
    const max = getMax(n, k);
    if (!max) return [0];

    return [getCount(n, k), getMin(n, k), max];
}

alert(luckyNumbers(10, 3));