import math
n=int(input())
f=[[1, 1], [1, 0]]
MOD=10**9+7
def mul(a, b):
    ret=[[0, 0], [0, 0]]
    for i in range(2):
        for j in range(2):
            for k in range(2):
                ret[i][j]+=a[i][k]*b[k][j]
    return ret
def powmod(a, k, mod):
    ret=[[1, 0], [0, 1]]
    ap=a
    while k>0:
        if k&1:
            ret=mul(ret, ap)
            for i in range(2):
                for j in range(2):
                    ret[i][j]%=mod
        ap=mul(ap, ap)
        for i in range(2):
            for j in range(2):
                ap[i][j]%=mod
        k>>=1
    return ret
ans=1
def lcm(a, b):
    return a//math.gcd(a, b)*b
for i in range(n):
    p, k=map(int, input().split())
    mod=p**k
    e=(p**(2*k-2))*(p*p-1)
    x=p-1
    fac=[]
    for j in range(2, x+1):
        if j*j>x:
            break
        if x%j==0:
            t=0
            while x%j==0:
                x//=j
                t+=1
            fac.append([j, t])
    if x>1:
        fac.append([x, 1])
    x=p+1
    for j in range(2, x+1):
        if j*j>x:
            break
        if x%j==0:
            t=0
            while x%j==0:
                x//=j
                t+=1
            if j==2:
                fac[0][1]+=t
            else:
                fac.append([j, t])
    if x>1:
        fac.append([x, 1])
    for j in range(2*k-2):
        e//=p
        fp=powmod(f, e, mod)
        if fp[0][0]==1 and fp[1][0]==0:
            continue
        e*=p
        break
    for q in fac:
        for j in range(q[1]):
            e//=q[0]
            fp=powmod(f, e, mod)
            if fp[0][0]==1 and fp[1][0]==0:
                continue
            e*=q[0]
            break
    ans=lcm(ans, e)
print(ans%MOD)