1276_B. Two Fairs_18915
There are n cities in Berland and some pairs of them are connected by two-way roads. It is guaranteed that you can pass from any city to any other, moving along the roads. Cities are numerated from 1 to n.

Two fairs are currently taking place in Berland — they are held in two different cities a and b (1 ≤ a, b ≤ n; a ≠ b).

Find the number of pairs of cities x and y (x ≠ a, x ≠ b, y ≠ a, y ≠ b) such that if you go from x to y you will have to go through both fairs (the order of visits doesn't matter). Formally, you need to find the number of pairs of cities x,y such that any path from x to y goes through a and b (in any order).

Print the required number of pairs. The order of two cities in a pair does not matter, that is, the pairs (x,y) and (y,x) must be taken into account only once.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 4⋅10^4) — the number of test cases in the input. Next, t test cases are specified.

The first line of each test case contains four integers n, m, a and b (4 ≤ n ≤ 2⋅10^5, n - 1 ≤ m ≤ 5⋅10^5, 1 ≤ a,b ≤ n, a ≠ b) — numbers of cities and roads in Berland and numbers of two cities where fairs are held, respectively.

The following m lines contain descriptions of roads between cities. Each of road description contains a pair of integers u_i, v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i) — numbers of cities connected by the road.

Each road is bi-directional and connects two different cities. It is guaranteed that from any city you can pass to any other by roads. There can be more than one road between a pair of cities.

The sum of the values of n for all sets of input data in the test does not exceed 2⋅10^5. The sum of the values of m for all sets of input data in the test does not exceed 5⋅10^5.

Output

Print t integers — the answers to the given test cases in the order they are written in the input.

Example

Input


3
7 7 3 5
1 2
2 3
3 4
4 5
5 6
6 7
7 5
4 5 2 3
1 2
2 3
3 4
4 1
4 2
4 3 2 1
1 2
2 3
4 1


Output


4
0
1
def main():
    
    t=int(input())
    allans=[]
    for _ in range(t):
        n,m,a,b=readIntArr()
        adj=[[] for __ in range(n+1)]
        for __ in range(m):
            u,v=readIntArr()
            adj[u].append(v)
            adj[v].append(u)
        
        def reachableFromAWOPassingB(a,b):
            st=[a]
            reachable=[False for _ in range(n+1)]
            reachable[a]=True
            while st:
                node=st.pop()
                for nex in adj[node]:
                    if nex!=b and not reachable[nex]:
                        reachable[nex]=True
                        st.append(nex)
            reachable[a]=False
            return reachable
        vA=reachableFromAWOPassingB(a,b)
        vB=reachableFromAWOPassingB(b,a)
        
        aCnt=0
        bCnt=0
        for i in range(1,n+1):
            if vA[i] and not vB[i]:
                aCnt+=1
            if not vA[i] and vB[i]:
                bCnt+=1
        ans=aCnt*bCnt
        allans.append(ans)
    multiLineArrayPrint(allans)
    
    return
    
import sys
# input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
 
def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultVal,dimensionArr): # eg. makeArr(0,[n,m])
    dv=defaultVal;da=dimensionArr
    if len(da)==1:return [dv for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(x,y):
    print('? {} {}'.format(x,y))
    sys.stdout.flush()
    return int(input())
 
def answerInteractive(ans):
    print('! {}'.format(ans))
    sys.stdout.flush()
 
inf=float('inf')
MOD=10**9+7
 
 
for _abc in range(1):
    main()
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.

### Description:
There are n cities in Berland and some pairs of them are connected by two-way roads. It is guaranteed that you can pass from any city to any other, moving along the roads. Cities are numerated from 1 to n.

Two fairs are currently taking place in Berland — they are held in two different cities a and b (1 ≤ a, b ≤ n; a ≠ b).

Find the number of pairs of cities x and y (x ≠ a, x ≠ b, y ≠ a, y ≠ b) such that if you go from x to y you will have to go through both fairs (the order of visits doesn't matter). Formally, you need to find the number of pairs of cities x,y such that any path from x to y goes through a and b (in any order).

Print the required number of pairs. The order of two cities in a pair does not matter, that is, the pairs (x,y) and (y,x) must be taken into account only once.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 4⋅10^4) — the number of test cases in the input. Next, t test cases are specified.

The first line of each test case contains four integers n, m, a and b (4 ≤ n ≤ 2⋅10^5, n - 1 ≤ m ≤ 5⋅10^5, 1 ≤ a,b ≤ n, a ≠ b) — numbers of cities and roads in Berland and numbers of two cities where fairs are held, respectively.

The following m lines contain descriptions of roads between cities. Each of road description contains a pair of integers u_i, v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i) — numbers of cities connected by the road.

Each road is bi-directional and connects two different cities. It is guaranteed that from any city you can pass to any other by roads. There can be more than one road between a pair of cities.

The sum of the values of n for all sets of input data in the test does not exceed 2⋅10^5. The sum of the values of m for all sets of input data in the test does not exceed 5⋅10^5.

Output

Print t integers — the answers to the given test cases in the order they are written in the input.

Example

Input


3
7 7 3 5
1 2
2 3
3 4
4 5
5 6
6 7
7 5
4 5 2 3
1 2
2 3
3 4
4 1
4 2
4 3 2 1
1 2
2 3
4 1


Output


4
0
1

### Input:
3
7 7 3 5
1 2
2 3
3 4
4 5
5 6
6 7
7 5
4 5 2 3
1 2
2 3
3 4
4 1
4 2
4 3 2 1
1 2
2 3
4 1

### Output:
4
0
1


### Input:
3
7 7 3 5
1 2
2 3
3 4
4 5
5 6
6 7
7 5
4 5 2 3
1 2
2 3
4 4
4 1
4 2
4 3 2 1
1 2
2 3
4 1

### Output:
4
0
1


### Code:
def main():
    
    t=int(input())
    allans=[]
    for _ in range(t):
        n,m,a,b=readIntArr()
        adj=[[] for __ in range(n+1)]
        for __ in range(m):
            u,v=readIntArr()
            adj[u].append(v)
            adj[v].append(u)
        
        def reachableFromAWOPassingB(a,b):
            st=[a]
            reachable=[False for _ in range(n+1)]
            reachable[a]=True
            while st:
                node=st.pop()
                for nex in adj[node]:
                    if nex!=b and not reachable[nex]:
                        reachable[nex]=True
                        st.append(nex)
            reachable[a]=False
            return reachable
        vA=reachableFromAWOPassingB(a,b)
        vB=reachableFromAWOPassingB(b,a)
        
        aCnt=0
        bCnt=0
        for i in range(1,n+1):
            if vA[i] and not vB[i]:
                aCnt+=1
            if not vA[i] and vB[i]:
                bCnt+=1
        ans=aCnt*bCnt
        allans.append(ans)
    multiLineArrayPrint(allans)
    
    return
    
import sys
# input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
 
def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultVal,dimensionArr): # eg. makeArr(0,[n,m])
    dv=defaultVal;da=dimensionArr
    if len(da)==1:return [dv for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(x,y):
    print('? {} {}'.format(x,y))
    sys.stdout.flush()
    return int(input())
 
def answerInteractive(ans):
    print('! {}'.format(ans))
    sys.stdout.flush()
 
inf=float('inf')
MOD=10**9+7
 
 
for _abc in range(1):
    main()