struct Scanner {
    private var stack = [String]()
    private var index = 0
    
    mutating func peek() -> String {
        if stack.count == index {
            stack += readLine()!.split(separator: " ").map{ String($0) }
        }
        return stack[index]
    }
    
    mutating func next() -> String {
        let value = peek()
        index += 1
        return value
    }
    
    mutating func nextInt() -> Int {
        return Int(next())!
    }
    
    mutating func nextDouble() -> Double {
        return Double(next())!
    }
}

let MOD = 1000000007

struct Zn {
    let n: Int
    
    init(_ n: Int) {
        self.n = n
    }
    
    static func + (lhs: Self, rhs: Self) -> Self {
        let n = lhs.n + rhs.n
        return Zn(n < MOD ? n : n - MOD)
    }
    
    static func - (lhs: Self, rhs: Self) -> Self {
        Zn((lhs.n - rhs.n + MOD) % MOD)
    }
    
    static func * (lhs: Self, rhs: Self) -> Self {
        Zn((lhs.n * rhs.n) % MOD)
    }
    
    static func += (lhs: inout Self, rhs: Self) {
        lhs = lhs + rhs
    }
}

let U = 6 * 6 * 6

struct Matrix {
    var A = [Zn](repeating: Zn(0), count: U * U)
   
    subscript(k: (Int, Int)) -> Zn {
        get {
            return A[k.0 * U + k.1]
        }
        set {
            A[k.0 * U + k.1] = newValue
        }
    }
    
    static var E: Self {
        var value = Matrix()
        for i in 0 ..< U {
            value[(i, i)] = Zn(1)
        }
        return value
    }
    
    static func * (lhs: Self, rhs: Self) -> Self {
        var value = Matrix()
        for i in 0 ..< U {
            for j in 0 ..< U {
                for k in 0 ..< U {
                    value[(i, j)] += lhs[(i, k)] * rhs[(k, j)]
                }
            }
        }
        return value
    }
    
    func pow(_ k: Int) -> Self {
        if k == 0 {
            return .E
        } else if k % 2 == 1 {
            return self.pow(k - 1) * self
        } else {
            return (self * self).pow(k / 2)
        }
    }
}

var scanner = Scanner()
let K = scanner.nextInt()
let M = scanner.nextInt()
let N = scanner.nextInt()

var matrix = Matrix()

func index(_ i: Int, _ j: Int, _ k: Int) -> Int {
    (i * 6 + j) * 6 + k
}

var table = [Bool](repeating: false, count: 6 * 6 * 6)

for _ in 0 ..< M {
    let P = scanner.nextInt() - 1
    let Q = scanner.nextInt() - 1
    let R = scanner.nextInt() - 1
    table[index(P, Q, R)] = true
}

for i in 0 ..< K {
    for j in 0 ..< K {
        for k in 0 ..< K {
            for l in 0 ..< K {
                if table[index(j, k, l)] {
                    matrix[(index(j, k, l), index(i, j, k))] += Zn(1)
                }
            }
        }
    }
}

matrix = matrix.pow(N - 3)

var answer = Zn(0)
for i in 0 ..< U where i % 6 == 0 {
    for j in 0 ..< U where table[j] && j / 36 == 0 {
        answer += matrix[(i, j)]
    }
}
print(answer.n)