CF1607B.Odd Grasshopper

The grasshopper is located on the numeric axis at the point with coordinate $x_0$.

Having nothing else to do he starts jumping between integer points on the axis. Making a jump from a point with coordinate $x$ with a distance $d$ to the left moves the grasshopper to a point with a coordinate $x - d$, while jumping to the right moves him to a point with a coordinate $x + d$.

The grasshopper is very fond of positive integers, so for each integer $i$ starting with $1$ the following holds: exactly $i$ minutes after the start he makes a jump with a distance of exactly $i$. So, in the first minutes he jumps by $1$, then by $2$, and so on.

The direction of a jump is determined as follows: if the point where the grasshopper was before the jump has an even coordinate, the grasshopper jumps to the left, otherwise he jumps to the right.

For example, if after $18$ consecutive jumps he arrives at the point with a coordinate $7$, he will jump by a distance of $19$ to the right, since $7$ is an odd number, and will end up at a point $7 + 19 = 26$. Since $26$ is an even number, the next jump the grasshopper will make to the left by a distance of $20$, and it will move him to the point $26 - 20 = 6$.

Find exactly which point the grasshopper will be at after exactly $n$ jumps.

蚱蜢位于数轴上坐标为 $x_0$ 的点处。

由于无事可做，它开始在数轴上的整数点之间跳跃。从坐标为 $x$ 的点向左跳跃距离 $d$，会使其到达坐标为 $x - d$ 的点；向右跳跃则会使其到达坐标为 $x + d$ 的点。

蚱蜢非常喜爱正整数，因此对每个从 $1$ 开始的整数 $i$，均有如下规律：恰好在起跳后第 $i$ 分钟，它执行一次距离恰好为 $i$ 的跳跃。也就是说，它在第 $1$ 分钟跳跃距离 $1$，第 $2$ 分钟跳跃距离 $2$，依此类推。

每次跳跃的方向按如下规则确定：若蚱蜢在跳跃前所在点的坐标为偶数，则向左跳跃；否则向右跳跃。

例如，若蚱蜢经过连续 $18$ 次跳跃后到达坐标为 $7$ 的点，则它将在第 $19$ 分钟向右跳跃距离 $19$（因为 $7$ 是奇数），最终到达点 $7 + 19 = 26$。由于 $26$ 是偶数，下一次（即第 $20$ 次）跳跃将向左进行，距离为 $20$，从而到达点 $26 - 20 = 6$。

求蚱蜢在恰好完成 $n$ 次跳跃后所处的坐标。

The first line of input contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

Each of the following $t$ lines contains two integers $x_0$ ($-10^{14} \leq x_0 \leq 10^{14}$) and $n$ ($0 \leq n \leq 10^{14}$) — the coordinate of the grasshopper's initial position and the number of jumps.

输入的第一行包含一个整数 $t$（$1 \leq t \leq 10^4$）—— 测试用例的数量。

接下来的 $t$ 行，每行包含两个整数 $x_0$（$-10^{14} \leq x_0 \leq 10^{14}$）和 $n$（$0 \leq n \leq 10^{14}$）—— 分别表示蚱蜢的初始位置坐标和跳跃次数。

Print exactly $t$ lines. On the $i$-th line print one integer — the answer to the $i$-th test case — the coordinate of the point the grasshopper will be at after making $n$ jumps from the point $x_0$.

精确输出 $t$ 行。第 $i$ 行输出一个整数——第 $i$ 个测试用例的答案，即蚱蜢从初始点 $x_0$ 出发，经过 $n$ 次跳跃后所到达的点的坐标。

The first two test cases in the example correspond to the first two jumps from the point $x_0 = 0$.

Since $0$ is an even number, the first jump of length $1$ is made to the left, and the grasshopper ends up at the point $0 - 1 = -1$.

Then, since $-1$ is an odd number, a jump of length $2$ is made to the right, bringing the grasshopper to the point with coordinate $-1 + 2 = 1$.

示例中的前两个测试用例对应于从点 $x_0 = 0$ 出发的前两次跳跃。

由于 $0$ 是偶数，第一次长度为 $1$ 的跳跃向左进行，蚱蜢最终落在点 $0 - 1 = -1$ 处。

接着，由于 $-1$ 是奇数，第二次长度为 $2$ 的跳跃向右进行，将蚱蜢带到坐标为 $-1 + 2 = 1$ 的点。