class Solution {
    private static final long MOD = 1000000007;

    public int numRollsToTarget(int n, int k, int target) {
        // out of bounds
        if (n > target || target > n * k) {
            return 0;
        }

        long[][] dp = new long[n + 1][target + 1];
        dp[0][0] = 1;

        for (int toss = 1; toss <= n; ++toss) {
            for (
                int sumIdx = toss, maxSumIdx = Math.min(target, toss * k);
                sumIdx <= maxSumIdx;
                ++sumIdx
            ) {
                for (int f = 1; f <= Math.min(k, sumIdx); ++f) {
                    dp[toss][sumIdx] = (dp[toss][sumIdx] + dp[toss - 1][sumIdx - f]) % MOD;
                }
            }
        }

        return (int) dp[n][target];
    }
}