/**
 * DP - Bottom Up
 * Array - Tabulation
 * Time O(N * MIN(N, M)) | Space O(MIN(N, M))
 * @param {number} steps
 * @param {number} arrLen
 * @return {number}
 */
var numWays = (steps, arrLen) => {
    const mod = ((10 ** 9) + 7);
    const length = Math.min(((steps >> 1) + 1), arrLen);

    let tabu = initTabu(length);
    tabu[1] = 1;

    for (let step = steps; (0 < step); step--) {
        const prev = initTabu(length);

        for (let pos = 1; (pos <= length); pos++) {
            prev[pos] = (
                tabu[pos - 1]
                + tabu[pos]
                + tabu[pos + 1]
            ) % mod;
        }

        tabu = prev;
    }

    return tabu[1];    
};

var initTabu = (length) => new Array(length + 2).fill(0);