from typing import List, Tuple


def solve(x: int, y: int, a: int) -> int:
    fromX: List[Tuple[int, int]] = []
    c: int = 0
    while 0 < x:
        fromX.append((x, c))
        x //= a
        c += 1
    fromX.append((x, c))

    dp: List[Tuple[int, int, int]] = [(y, 0, 1e9)]
    while 1:
        [i, j, k] = dp[-1]
        d, r = i // a, i % a
        if r == 0:
            dp.append((d,
                       min(j + 1, k + 2),
                       k + a))
        elif r == a - 1:
            dp.append((d,
                       j + a,
                       min(j + 2, k + 1)))
        else:
            dp.append((d,
                      min(j + r + 1, k + (r + 1) + 1),
                      min(j + (a - r) + 1, k + (a - (r + 1)) + 1)))
        if i == 0:
            break

    fromY = []
    for i, j, k in dp:
        fromY.append((i + 1, k))
        fromY.append((i, j))

    def toX(n: int) -> int:
        return min(map(lambda b: abs(b[0] - n) + b[1], fromX))

    ans = 1e9
    if len(fromX) < 2:
        for i, j in fromX:
            ans = min(ans, *map(lambda p: abs(p[0] - i) + p[1] + j, fromY))
    else:
        k = 2
        for i, j in fromY:
            while i < fromX[k][0] and k + 1 < len(fromX):
                k += 1
            ans = min(ans,
                      abs(i - fromX[k - 2][0]) + j + fromX[k - 2][1],
                      abs(i - fromX[k - 1][0]) + j + fromX[k - 1][1],
                      abs(i - fromX[k][0]) + j + fromX[k][1])
    return ans


def main():
    T = int(input())
    for _ in range(T):
        print(solve(*map(int, input().split())))


if __name__ == '__main__':
    main()