Problem: Ringo Mart, a convenience store, sells apple juice.

On the opening day of Ringo Mart, there were A cans of juice in stock in the morning. Snuke buys B cans of juice here every day in the daytime. Then, the manager checks the number of cans of juice remaining in stock every night. If there are C or less cans, D new cans will be added to the stock by the next morning.

Determine if Snuke can buy juice indefinitely, that is, there is always B or more cans of juice in stock when he attempts to buy them. Nobody besides Snuke buy juice at this store.

Note that each test case in this problem consists of T queries.

Constraints

* 1 \leq T \leq 300
* 1 \leq A, B, C, D \leq 10^{18}
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


T
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_T B_T C_T D_T


In the i-th query, A = A_i, B = B_i, C = C_i, D = D_i.

Output

Print T lines. The i-th line should contain `Yes` if Snuke can buy apple juice indefinitely in the i-th query; `No` otherwise.

Examples

Input

14
9 7 5 9
9 7 6 9
14 10 7 12
14 10 8 12
14 10 9 12
14 10 7 11
14 10 8 11
14 10 9 11
9 10 5 10
10 10 5 10
11 10 5 10
16 10 5 10
1000000000000000000 17 14 999999999999999985
1000000000000000000 17 15 999999999999999985


Output

No
Yes
No
Yes
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes


Input

24
1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 3 4 1
2 4 1 3
2 4 3 1
3 1 2 4
3 1 4 2
3 2 1 4
3 2 4 1
3 4 1 2
3 4 2 1
4 1 2 3
4 1 3 2
4 2 1 3
4 2 3 1
4 3 1 2
4 3 2 1


Output

No
No
No
No
No
No
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
No
No
No

Solution (in PYTHON3):

Solution:
import fractions


def run(t, a, b, c, d):
    ret = []
    for i in range(t):
        ret.append(check(a[i], b[i], c[i], d[i]))
    return ret


def check(a, b, c, d):
    if a < b:
        return 'No'
    if d < b:
        return 'No'
    if c < b:
        g = fractions.gcd(b, d)
        amodb = a % b
        if g == 1:
            if b - 1 > c:
                return 'No'
        elif g == b:
            if amodb > c:
                return 'No'
        else:
            if (b - g) > c:
                return 'No'
    return 'Yes'


def read_line():
    t = int(input())
    a = []
    b = []
    c = []
    d = []
    for i in range(t):
        at, bt, ct, dt = list(map(int, input().split()))
        a.append(at)
        b.append(bt)
        c.append(ct)
        d.append(dt)
    return (t, a, b, c, d)


def main():
    t, a, b, c, d = read_line()
    ret = run(t, a, b, c, d)
    for i in range(t):
        print(ret[i])


if __name__ == '__main__':
    main()