Problem:
Score : 100 points

Problem Statement

In this problem, you should process T testcases.

For each testcase, you are given four integers N, M, A, B.

Calculate \sum_{i = 0}^{N - 1} floor((A \times i + B) / M).

Constraints

1 \leq T \leq 100,000

1 \leq N, M \leq 10^9

0 \leq A, B < M

Input

Input is given from Standard Input in the following format:

T
N_0 M_0 A_0 B_0
N_1 M_1 A_1 B_1
:
N_{T - 1} M_{T - 1} A_{T - 1} B_{T - 1}

Output

Print the answer for each testcase.

Sample Input 1

5
4 10 6 3
6 5 4 3
1 1 0 0
31415 92653 58979 32384
1000000000 1000000000 999999999 999999999

Sample Output 1

3
13
0
314095480
499999999500000000

Solution in Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func Scan() string {
	sc.Scan()
	return sc.Text()
}
func rScan() []rune {
	return []rune(Scan())
}
func iScan() int {
	n, _ := strconv.Atoi(Scan())
	return n
}
func fScan() float64 {
	n, _ := strconv.ParseFloat(Scan(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func SScan(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scan()
	}
	return a
}
func iSScan(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = iScan()
	}
	return a
}
func abs(x int) int {
	if x < 0 {
		x = -x
	}
	return x
}
func mod(x, d int) int {
	x %= d
	if x < 0 {
		x += d
	}
	return x
}
func larger(a, b int) int {
	if a < b {
		return b
	} else {
		return a
	}
}
func smaller(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}
func max(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x < a[i] {
			x = a[i]
		}
	}
	return x
}
func min(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x > a[i] {
			x = a[i]
		}
	}
	return x
}
func sum(a []int) int {
	x := 0
	for _, v := range a {
		x += v
	}
	return x
}
func fSum(a []float64) float64 {
	x := 0.
	for _, v := range a {
		x += v
	}
	return x
}
func bPrint(f bool, x string, y string) {
	if f {
		fmt.Println(x)
	} else {
		fmt.Println(y)
	}
}
func iSSPrint(x []int) {
	fmt.Println(strings.Trim(fmt.Sprint(x), "[]"))
}

var lp1 int = 1000000007
var lp2 int = 998244353

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, lp1)
	sc.Split(bufio.ScanWords)
	t := iScan()
	for i := 0; i < t; i++ {
		fmt.Println(floorSum(iScan(), iScan(), iScan(), iScan()))
	}
}

func floorSum(n, m, a, b int) int {
	ret := 0
	if a >= m {
		ret += (n - 1) * n * (a / m) / 2
		a %= m
	}
	if b >= m {
		ret += n * (b / m)
		b %= m
	}
	ymx := (a*n + b) / m
	xmx := ymx*m - b
	if ymx == 0 {
		return ret
	}
	ret += (n - (xmx+a-1)/a) * ymx
	ret += floorSum(ymx, a, m, (a-xmx%a)%a)
	return ret
}
func crt(r, m []int) [2]int {
	n := len(r)
	r0, m0 := 0, 1
	for i := 0; i < n; i++ {
		r1 := safeMod(r[i], m[i])
		m1 := m[i]
		if m0 < m1 {
			r0, r1 = r1, r0
			m0, m1 = m1, m0
		}
		if m0%m1 == 0 {
			if r0%m1 != r1 {
				return [2]int{0, 0}
			}
			continue
		}
		tmp := invGcd(m0, m1)
		g, im := tmp[0], tmp[1]
		u1 := m1 / g
		if (r1-r0)%g != 0 {
			return [2]int{0, 0}
		}
		x := (r1 - r0) / g % u1 * im % u1
		r0 += x * m0
		m0 *= u1
		if r0 < 0 {
			r0 += m0
		}
	}
	return [2]int{r0, m0}
}

func powMod(x, n, m int) int {
	if m == 1 {
		return 0
	}
	r := 1
	y := x % m
	if y < 0 {
		y += m
	}
	for n != 0 {
		if (n & 1) == 1 {
			r = (r * y) % m
		}
		y = (y * y) % m
		n >>= 1
	}
	return r
}
func safeMod(x, d int) int {
	x %= d
	if x < 0 {
		x += d
	}
	return x
}
func invMod(x, m int) int {
	z := invGcd(x, m)
	return z[1]
}
func invGcd(a, b int) [2]int {
	a = a % b
	if a < 0 {
		a += b
	}
	s, t := b, a
	m0, m1 := 0, 1
	for t != 0 {
		u := s / t
		s -= t * u
		m0 -= m1 * u
		tmp := s
		s = t
		t = tmp
		tmp = m0
		m0 = m1
		m1 = tmp
	}
	if m0 < 0 {
		m0 += b / s
	}
	return [2]int{s, m0}
}
func primitiveRoot(m int) int {
	if m == 2 {
		return 1
	} else if m == 167772161 {
		return 3
	} else if m == 469762049 {
		return 3
	} else if m == 754974721 {
		return 11
	} else if m == 998244353 {
		return 3
	}
	divs := make([]int, 20)
	divs[0] = 2
	cnt := 1
	x := (m - 1) / 2
	for (x % 2) == 0 {
		x /= 2
	}
	for i := 3; i*i <= x; i += 2 {
		if x%i == 0 {
			divs[cnt] = i
			cnt++
			for x%i == 0 {
				x /= i
			}
		}
	}
	if x > 1 {
		divs[cnt] = x
		cnt++
	}
	for g := 2; ; g++ {
		ok := true
		for i := 0; i < cnt; i++ {
			if powMod(g, (m-1)/divs[i], m) == 1 {
				ok = false
				break
			}
		}
		if ok {
			return g
		}
	}
}