Kertoma

const inp = require("fs").readFileSync(0, "utf8").trim();

const length = inp.split(" ").map(Number).reduce((a, c) => a + c, 0);

/**
 * @param {number} n 
 * @returns {string}
 */
function countNumbers(n) {
    const ns = n.toString();
    const map = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    for (const char of ns) map[char]++;
    return map.join(" ");
}

let s = 2;
let n = 2;

// handle smaller numbers
while (n !== 10) {
    if (s.toString().length === length && countNumbers(s) === inp) {
        console.log(n.toString());
        process.exit(0);
    }
    n++;
    s *= n;
}

// handle bigger numbers
let l = s.toString().length;
while (true) {
    const added = Math.log10(n) | 0;
    const extra = (Math.log10(s) + 1 | 0) - (7 + added);
    s = (s / (10 ** (added + extra))) | 0;
    l += added + extra;
    if (l === length) {
        console.log(n.toString());
        process.exit(0);
    }
    n++;
    s *= n;
}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 1, 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED

Test 16

Group: 3

Verdict: ACCEPTED