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You can do the same with the second and third equations and solve the resulting three-by-three system, how to break up a couple from a distance

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mod = 10**9

for cas in xrange(input()): a,b,c,d,e,f,g,h,n = map(int, raw_input().strip().split())

X = max(a,f,g)
Y = max(e,b,c)
XY = X+Y
XY0 = XY+0
XY1 = XY+1
XY2 = XY+2
XY3 = XY+3

N = XY+4
n += 1
a -= 1
b -= 1
c -= 1
e -= 1
f -= 1
g -= 1

temp = [[0]*N for i in xrange(N)]
pA = [[0]*N for i in xrange(N)]
temprow = [0]*N

def mulA():
    for r in xrange(N):
        pAr = pA[r]
        for j in xrange(N):
            temprow[j] = 0

        temprow[  a] += pAr[0]
        temprow[X+b] += pAr[0]
        temprow[X+c] += pAr[0]
        temprow[XY1] += pAr[0]
        temprow[X+e] += pAr[X]
        temprow[  f] += pAr[X]
        temprow[  g] += pAr[X]
        temprow[XY3] += pAr[X]
        temprow[XY0] += d * pAr[XY0]
        temprow[XY0] += d * pAr[XY1]
        temprow[XY1] += d * pAr[XY1]
        temprow[XY2] += h * pAr[XY2]
        temprow[XY2] += h * pAr[XY3]
        temprow[XY3] += h * pAr[XY3]
        for i in xrange(X-1): temprow[  i] += pAr[  i+1]
        for i in xrange(Y-1): temprow[X+i] += pAr[X+i+1]

        for j in xrange(N):
            pAr[j] = temprow[j] % mod

def sqr():
    global temp, pA
    for i in xrange(N):
        tempi = temp[i]
        pAi = pA[i]
        for j in xrange(N):
            tempi[j] = 0

        for k in xrange(N):
            pAik = pAi[k]
            if pAik:
                pAk = pA[k]
                for j in xrange(N):
                    tempi[j] += pAik * pAk[j]

        for j in xrange(N):
            tempi[j] %= mod

    temp, pA = pA, temp


def powA(n):
    if n == 0:
        return
    elif n & 1:
        powA(n-1)
        mulA()
    else:
        powA(n/2)
        sqr()

for i in xrange(N):
    pA[i][i] = 1

powA(n)

x = y = 0
for j in xrange(XY):
    x += pA[0][j]
    y += pA[X][j]
x += pA[0][XY0] + pA[0][XY2]
y += pA[X][XY0] + pA[X][XY2]
x %= mod
y %= mod

print x, y