// Package q3129 implements a solution for https://leetcode.com/problems/find-all-possible-stable-binary-arrays-i/
package q3129

const MOD = 1e9 + 7

func alloc(zeros, ones int) [][][2]int {
	buf := make([][2]int, (zeros+1)*(ones+1))
	ret := make([][][2]int, zeros+1)
	for i := range ret {
		ret[i] = buf[i*(ones+1) : (i+1)*(ones+1)]
	}
	return ret
}

func numberOfStableArrays(zeros, ones, limit int) int {
	dp := alloc(zeros, ones)
	// dimensions: [zeros][ones][last_digit]

	for z := 1; z <= min(limit, zeros); z++ {
		dp[z][0][0] = 1
	}
	for o := 1; o <= min(limit, ones); o++ {
		dp[0][o][1] = 1
	}
	for z := 1; z <= zeros; z++ {
		for o := 1; o <= ones; o++ {
			dp[z][o][0] = dp[z-1][o][1] + dp[z-1][o][0]
			if z > limit {
				dp[z][o][0] -= dp[z-1-limit][o][1]
			}

			dp[z][o][1] = dp[z][o-1][0] + dp[z][o-1][1]
			if o > limit {
				dp[z][o][1] -= dp[z][o-1-limit][0]
			}

			dp[z][o][0] = (dp[z][o][0] + MOD) % MOD
			dp[z][o][1] = (dp[z][o][1] + MOD) % MOD
		}
	}

	return (dp[zeros][ones][0] + dp[zeros][ones][1]) % MOD
}

var _ = numberOfStableArrays