Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.

Input

The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.

Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Output

Print the only integer s — the value g(n)(x) modulo 109 + 7.

Examples

Input

3 4 1 1


Output

7


Input

3 4 2 1


Output

25


Input

3 4 3 1


Output

79
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
 
import java.util.InputMismatchException;
 
public class cf_practise{
static long d=1000000007;
static long check(long a)
{
if(a>d)
return a%d;
else return a;}

public static void main(String args[]) {
InputReader in = new InputReader(System.in);
 
//OutputWriter st = new OutputWriter(System.out);
long a,b,x,n;
long ans=0;
a=in.readInt();
b=in.readInt();

n=in.readLong();
x=in.readInt();
if(a==1)
ans=check(x+check(check(n)*b));
else
{
long c=exp(a,n);
ans=check(check(c*x)+check(b*check((c-1)*exp(a-1,d-2))));
}
System.out.println(ans);
//st.printLine(Math.min(ans2,ans1));
//st.close();

}
static long exp(long a,long b)
{
if(b==1)
return a;
 
if(b%2==0)
{
long c=exp(a,b/2);
long e=c*c;
return (e%d);
}
 
else
{
long c=exp(a,b/2);
long e=c*c;e%=d;
e*=a;
return (e%d);
}}}

class InputReader {
 
private InputStream stream;
 
private byte[] buf = new byte[1024];
 
private int curChar;
 
private int numChars;
 
private SpaceCharFilter filter;
 
public InputReader(InputStream stream) {
 
this.stream = stream;
 
}
 
public int read() {
 
if (numChars == -1) {
throw new InputMismatchException();
}
 
if (curChar >= numChars) {
 
curChar = 0;
 
try {
 
numChars = stream.read(buf);
 
} catch (IOException e) {
 
throw new InputMismatchException();
 
}
 
if (numChars <= 0) {
return -1;
}
 
}
return buf[curChar++];
 
}
 
public int readInt() {
 
int c = read();
 
while (isSpaceChar(c)) {
c = read();
}
 
int sgn = 1;
 
if (c == '-') {
 
sgn = -1;
 
c = read();
 
}
 
int res = 0;
 
do {
 
if (c < '0' || c > '9') {
throw new InputMismatchException();
}
 
res *= 10;
res += c - '0';
 
c = read();
 
} while (!isSpaceChar(c));
 
return res * sgn;
 
}
 
public String readString() {
 
int c = read();
 
while (isSpaceChar(c)) {
c = read();
}
 
StringBuilder res = new StringBuilder();
 
do {
 
res.appendCodePoint(c);
 
c = read();
 
} while (!isSpaceChar(c));
 
return res.toString();
 
}
 
public double readDouble() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
double res = 0;
while (!isSpaceChar(c) && c != '.') {
if (c == 'e' || c == 'E') {
return res * Math.pow(10, readInt());
}
if (c < '0' || c > '9') {
throw new InputMismatchException();
}
res *= 10;
res += c - '0';
c = read();
}
if (c == '.') {
c = read();
double m = 1;
while (!isSpaceChar(c)) {
if (c == 'e' || c == 'E') {
return res * Math.pow(10, readInt());
}
if (c < '0' || c > '9') {
throw new InputMismatchException();
}
m /= 10;
res += (c - '0') * m;
c = read();
}
}
return res * sgn;
}
 
public long readLong() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
long res = 0;
do {
if (c < '0' || c > '9') {
throw new InputMismatchException();
}
res *= 10;
res += c - '0';
c = read();
} while (!isSpaceChar(c));
return res * sgn;
}
 
public boolean isSpaceChar(int c) {
 
if (filter != null) {
return filter.isSpaceChar(c);
}
 
return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
 
}
 
public String next() {
 
return readString();
}
 
public interface SpaceCharFilter {
 
public boolean isSpaceChar(int ch);
 
}
 
}
 
class OutputWriter {
 
private final PrintWriter writer;
 
public OutputWriter(OutputStream outputStream) {
 
writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
 
}
 
public OutputWriter(Writer writer) {
 
this.writer = new PrintWriter(writer);
 
}
 
public void print(Object... objects) {
 
for (int i = 0; i < objects.length; i++) {
 
if (i != 0) {
writer.print(' ');
}
writer.print(objects[i]);
 
}
 
}
 
public void printLine(Object... objects) {
 
print(objects);
 
writer.println();
 
}
 
public void close() {
 
writer.close();
 
}
 
public void flush() {
 
writer.flush();
 
}
 
}